Answer:
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!
