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Solve the equation 2x² + 2x + 12 = 3x² – x + 2.

A. x = –5, x = –2
B. x = 2, x = –5
C. x = 2, x = 5
D. x = –2, x = 5

User Haddon
by
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2 Answers

3 votes
Subtract 2x^2 from both sides, subtract 2x from both sides, subtract 12 from both sides
x^2 - 3x - 10 = 0
Factor
(x-5)(x+2)=0
x=5, x=-2
Answer D
User Carl Boisvert
by
5.0k points
2 votes

Answer:

D: x = -2, x = 5

Explanation:

To solve for a variable, you first have to isolate it on one side of the equation. Remember that whatever you do to one side, you also have to do to the other.

2x² + 2x + 12 = 3x² - x + 2 Subtract 2x² from both sides

2x + 12 = x² - x + 2 Subtract 2x from both sides

12 = x² - 3x + 2 Subtract 12 from both sides

0 = x² - 3x - 10 Using factoring, split this into two expressions

0 = (x - 5) (x + 2) Set each expression equal to 0

x - 5 = 0 and x + 2 = 0 Solve each expression

x = 5 and x = -2

Now, you can plug in both answers to check your work

2x² + 2x + 12 = 3x² - x + 2 Plug in 5

2(5)² + 2(5) + 12 = 3(5)² - 5 + 2 Simplify

2(25) + 10 + 12 = 3(25) - 5 + 2 Simplify some more

50 + 10 + 12 = 75 - 5 + 2 Simplify one more time

72 = 72 It works!

2x² + 2x + 12 = 3x² - x + 2 Plug in -2

2(-2)² +2(-2) + 12 = 3(-2)² -(-2) + 2 Simplify

2(4) - 4 + 12 = 3(4) + 2 + 2 Simplify again

8 - 4 + 12 = 12 + 2 + 2 Simplify one more time

16 = 16 It also works!

User Aizhan
by
5.3k points