Answer:
(x+3)² = 25
Step-by-step explanation:
Pre-Solving
We are given the following equation:
2x² + 12x = 32
We want to find what the equation of this will be when we complete the square.
Solving
To start, we can divide both sides by 2. The resulting equation will be:
x² + 6x = 16
When completing the square, we add a third number to both sides. This is because we will factor the left side into the form (a+b)².
Recall that (a+b)² = a² + 2ab + b². The 6x is the 2ab in this sense, but because the value of a would be x (a² is x²), 6 = 2b.
If we solve 6 = 2b, then b = 3.
Now, square it to get the third number in the equation. 3² = 9.
We now add 9 to both sides of the equation. We do this in order to balance the equation, because if we add 9 to only one side, the equation will become unbalanced.
x² + 6x + 9 = 16 + 9
x² + 6x + 9 = 25
We can factor the left side to get:
(x+3)² = 25