solve using the quadratic formula:
3x=2x^2-2

Answers

Answer 1

Answer:

[tex]x=2\\x=-\frac{1}{2}[/tex]

Step-by-step explanation:

1) Move terms to the left side.

[tex]3x=2x^{2} -2\\3x-(2x^{2}-2)=0[/tex]

2) Distribute.

[tex]3x-(2x^{2} -2)=0\\3x-2x^{2} +2=0[/tex]

3) Rearrange terms.

[tex]3x-2x^{2} +2=0\\-2x^{2} +3x+2=0[/tex]

4) Common factor.

[tex]-2x^{2} +3x+2=0\\-(2x^{2} -3x-2)=0[/tex]

5) Divide both sides of the equation by the same term.

[tex]-(2x^{2} -3x-2)=0\\2x^{2} -3x-2=0[/tex]

6) Use the quadratic formula.

[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

[tex]2x^{2} -3x-2=0\\a=2\\b=-3\\c=-2[/tex]

[tex]x=\frac{-(-3)+\sqrt{(-3)^{2} -4*2(-2)} }{2*2}[/tex]

7) Simplify.

Evaluate the exponent

[tex]x=\frac{3+\sqrt{(-3)^{2}-4*2(-2) } }{2*2}[/tex]

[tex]x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}[/tex]

Multiply the numbers

[tex]x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}[/tex]

[tex]x=\frac{3+\sqrt{9+16} }{2*2}[/tex]

Add the numbers

[tex]x=\frac{3+\sqrt{9+16} }{2*2}[/tex]

[tex]x=\frac{3+\sqrt{25} }{2*2}[/tex]

Evaluate the square root

[tex]x=\frac{3+\sqrt{25} }{2*2} \\x=\frac{3+5}{2*2}[/tex]

Multiply the numbers

[tex]x=\frac{3+5}{2*2}[/tex]

[tex]x=\frac{3+5}{4}[/tex]

8) Seperate the equations.

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

[tex]x=\frac{3+5}{4}[/tex]

[tex]x=\frac{3-5}{4}[/tex]

9) Solve.

Rearrange and isolate the variable to find each solution.

[tex]x=2\\x=-\frac{1}{2}[/tex]


Related Questions

Mr.Keaton planted 918 cornstalks there are 9 cornstalks in each row how many rows of corn did he plant

Answers

918 / 9 = 102 rows.

Answer:

I think 102 rows of corn

Step-by-step explanation:

918 ÷ 9 = 102


Taylor left to walk the dog at
4:25. She got back at 5:00. How
long was the dog's walk?

Answers

Answer:

Taylor walked 35 minutes

Step-by-step explanation:

4:25

+:35

=5:00.

once a clock hits 60 it's automatically turned to the next hour so since 25 + 35 = 50 it's automatically turned to 5:00

Solve (u+2)^2+6=69 , where u is a real number.

Answers

Answer:

5.94 and -9.94

Explanation:

Use complete the square to answer the question and then type the last line into a calculator to get 5.94 and -9.94

if f(x)=2x^2-1, then f(-3)=

Answers

Answer:

f(-3) =17

Step-by-step explanation:

f(x)=2x^2-1

Let x = -3

f(-3)=2(-3)^2-1

     = 2(9) -1

     = 18-1

     17

Help me please please

Answers

Answer:

a.11

b.20

c.44

d.5

e.60

f.12

g.4

h.40

i.900

j.6

Step-by-step explanation:

hope this helps

Which is an equation of the line through the origin and (-5,6)?
A. y=-5/6x
B. y=-6x
C. y=-5x
D. y=- 6/5x

Answers

Answer:

y=-6/5x

Step-by-step explanation:

What is the range of the function y = x^2?


Ox>0

O all real numbers

Oy>0​

Answers

Answer:

The range is y≥0

Step-by-step explanation:

The shape of this graph is a parabola

You may see this by using the Desmos calculator and typing y=x^2 if you would like to visualize.

(a) The function y = x^2 simply takes whatever number you feed it (x) and outputs x squared.

For example

y = (2)^2=4

y = (3)^2 = 9

(b) To graph x^2 simply make a table of values and plug in 0 -> however high you would like to go ( usually to 5 or so is fine but you could go to infinity).

Example

      y = x^2

                 Y    |     X

                ________

                 2      |   4  

                 3     |   9

                 4    |    16

In this case the function's range is y≥0 because all y values will be greater than or equal to 0.

If you are wanting to learn how to specifically graph this you can look up (Graphing y = x²) if my quick graphing explanation back at mark (b) does not help.

Burt ran the length of the trail in his town’s park. There are 9 parts to the trail, and each part is the same length. Burt ran a total of 1.8 kilometers.
What is the length of each part of the trail?

Answers

Answer:

.2 kilometers

Step-by-step explanation:

Since there are 9 parts to the trail and the total is 1.8 kilometers, just divide the total by how many parts. 1.8 divided by 9 is .2 so the length of each part of the trail is .2 kilometers

Determine whether each equation represents a proportional relationship.

Y=2.5x

y= x - 4

Answers

Answer:

y=2.5x - Proportional  

y= x - 4 - Not Proportional  

Step-by-step explanation:

A linear function that is proportional is in the form y =kx (k is the constant of variation) and passes the origin.

The first equation given is in this form (2.5 is the constant) and it passes through the origin. It is proportional.

However, the second one is not proportional is it does not pass the orgin and it's not in y=kx form.

Hope this helps.

7x – 5 – 3x = 7 – 6x solve for x

Answers

Step-by-step explanation:

7x - 3x=5 + 7

we will plus --

10x =12

x=12÷10 or 10 /12

x=12.2

ANSWER FAST PLZ I REALLY NEED HELP :(


Mr. Wiley averages 12 mph when his boat is in still water. One day he goes 12 miles upstream and the same distance back. The round-trip takes two hours and 15 minutes. What is the speed of the current on that day?

Answers

Answer:

  4 mph

Step-by-step explanation:

The current subtracts from the boat speed going upstream, and add going downstream. The relation between speed, distance, and time is ...

   time = distance/speed

  2 1/4 = 12/(12 -c) + 12/(12 +c) . . . . . round trip time is the sum of the trip times

  9/4(12 +c)(12 -c) = 12(12 +c) +12(12 -c) . . . . multiply by (12 +c)(12 -c)

  144 -c^2 = 128 . . . . . . multiply by 4/9 and simplify

  16 = c^2 . . . . . . . . . add c^2 -128

  c = 4 . . . . . . . . . positive square root

The current was 4 mph that day.

Which sentence is correct?
A. -4 > 3
B. -4< -6
C. -4 > -7
D. -5 > -4

Answers

Answer:

C. -4 > -7

Step-by-step explanation:

answer= option C

B. I think but i’m not sure

3(2/3p+3-1/3p-5) What is the simplified version of this equation.

Answers

Answer: p+1

Step-by-step explanation:

3(2/3p+3-1/3p)

=3(1/3p+3)

=p+1


1. Name a midsegment in the triangle.

Answers

Answer:

EF

Step-by-step explanation:

Hope this helps!

Hehhhhhhhhhhhhhheh eh

Answers

So smart✅ like the humor tho

Mark deposited $750 in a savings account earning 3% interest over 9 years. What was the total interest earned after 9 years?

Answers

Answer: The final balance is $982.47.

The total compound interest is $232.47.

Step-by-step explanation:

which graph appears to show a proportional relationship between x and y ​

Answers

Answer:

What graph?

Step-by-step explanation:

No wonder why you have been waiting 25+ mins to get an answer

find the value of 777^2 - 223^2​

Answers

Answer:

549440

Step-by-step explanation:

777^2 = 603729

223^2 = 54289

603729 - 54289 = 549440

Plzzzzz help meeeee plzzzz I really d answa

Answers

Answer:

c. is correct answer I think

34.2 is what percent of 288? Round to the nearest hundredth.

Answers

Answer:

11.87%

Step-by-step explanation:

34.2/288=0.11875

Which is about 0.1187

So 11.87%

Answer:

11.87

Step-by-step explanation:

mental math and just big brain

25)
Find the measure of each lettered angle.
The diagram is not drawn to scale.

Answers

Answer:

The Diagram is not showing

Step-by-step explanation:

check attachment for question

Answers

Answer:

[tex]\displaystyle 3x^2 + x[/tex]

Explanation:

All you are doing is combining like-terms:

[tex]\displaystyle \boxed{3x^2 + x} \Rightarrow [5x + x^2 - 1] + [2x^2 - 4x + 1][/tex]

I am joyous to assist you at any time.

Solve four ninths minus four tenths equals blank.

Answers

Answer:

2/45

Step-by-step explanation:

a coin is tossed 4 times. what is the probability of getting heads each time

Answers

answer: 1/16

If you flip a coin 4 times, the probability of getting all heads is 1/16.

URGENT
Evaluate the expression below for the given value

X^2+ 2x for x = -3

Answers

Answer:

-3×2+2×-3

-6+-6

-12

I think^=×

Answer:  3

Step-by-step explanation:

X^2+ 2x for x = -3

(-3)^2+ 2(-3)

(-3)(-3) -6

+9 -6

3

To get home, Renae can take one of four buses: #41. #28. #55, or #81. Once she is on a bus, she will randomly select one of the
following equally likely activities: listening to her music player, writing a letter, or reading a book. Her choice of bus and choice of entertainment are independen
events, because the bus that Renae took did not affect which activity she chose. For example, what is the probability that Renae writes a letter if she takes the
#41 bus? What is the probability that Renae writes a letter if she takes the #55 bus?

Answers

The probability that Renae writes a letter if she takes the #55 bus is 1/12

The buses are given as:

Buses: #41, #28, #55, #81

There are 4 buses of equal probabilities.

So, the probability that she takes the #55 is:

[tex]P(55)= \frac 14[/tex]

The activities are given as:

Activities: listening to her music player, writing a letter, or reading a book

There are 3 activities of equal probabilities.

So, the probability that she writes a letter is:

[tex]P(Letter)= \frac 13[/tex]

The probability that she does both independent events is:

[tex]Pr = P(55) \times P(Letter)[/tex]

So, we have:

[tex]Pr = \frac 14 \times \frac 13[/tex]

[tex]Pr = \frac 1{12}[/tex]

Hence, the probability is 1/12

Read more about probabilities at:

https://brainly.com/question/251701

There are visitors at home. Michelle made 10 and 3/5 cups of tea while Leslie made 9 and 2/5 cups of tea. How many cups of tea did the two sisters make for the visitors? *

Answers

Answer:

20 cups

Step-by-step explanation:

Michelle: 10 3/5 cups made

Leslie: 9 2/5 cups made

Steps:

First, let's turn each number into decimal form.

10 3/5 = 10.6

9 2/5 = 9.4

Then, add

9.4 + 10.6 = 20

Conclusion

They made 20 cups in all

Note:

Hope this helped :)

Have a nice day

Reply with any questions or concerns please :D

Ernie played 35 soccer games this season. He won 28 games. Enter the
percentage of games Ernie won.

Answers

28 / 35 first divide

= 0.8

Then multiply the decimal with 100

0.8 x 100

= 80

There fore the answer is 80%

Hope this helps!
Brainliest is much appreciated!

Answer:

I think it;s 9.8

Step-by-step explanation:

You divide 35 and 28 i think

Find the equation of the line passing through the point (-1,0) and parallel to the line
y=-1/2x+3/7

A) y= 2x + 2

B) y = -1/2-1/2

C) y = 1/2x+1/2

D) y = - 1/2x+1/2

Answers

Answer:

B) y= -½x -½

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

[tex]y = - \frac{1}{2} x + \frac{3}{7} [/tex]

Slope of given line= -½

Since parallel lines have the same slope, slope of unknown line= -½.

y= -½x +c

To find the value of c, substitute a pair of coordinates into the equation.

When x= -1, y= 0,

[tex]0 = - \frac{1}{2} ( - 1) + c[/tex]

[tex]0 = \frac{1}{2} + c[/tex]

[tex]c = - \frac{1}{2} [/tex]

Thus, the equation of the line is y= -½x -½.

Bret buys a dining table that costs $150 before tax. The sales tax is 8%. How much sales tax did he pay?

Answers

Answer:

$12

Step-by-step explanation:

to find sales tax you multiply the cost by the percentage

you do 150 * 8%

thats also 150 * 0.08

150 * 0.08 is 12

so you pay $12 in tax

Bret paid $12 as sales tax.

What is a expression? What is a mathematical equation? What is Equation Modelling? What is denominator?

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In a fraction say (x/y), [y] is called denominator.

We have Bret buys a dining table that costs $150 before tax. The sales tax is 8%.

Assume that he paid $[x] as sales tax. Then, we can write -

[x] = 8% of 150

[x] = (8/100) x 150

[x] = 12

Therefore, Bret paid $12 as sales tax.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ2

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