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

D: x = - 2, x = 5

Step-by-step 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!

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