Answer: x = 1, -13
Explanation:
We will solve this by completing the square, as asked in the instructions. If we do this correctly, we will end up with a perfect square that will allow us to solve more easily.
Given:
x² + 12x = 13
Set the equation equal to 0 by subtracting both sides of the equation by 13:
x² + 12x - 13 = 0
Group the first two terms:
(x² + 12x) - 13 = 0
Add and subtract
to the grouped terms:
(x² + 12x + 36 - 36) - 13 = 0
Regroup the terms, move the negative out and simplify:
(x² + 12x + 36) - 49 = 0
Factor the grouped terms (6 is our perfect square here):
(x + 6)(x + 6) - 49 = 0
Add 49 to both sides of the equation and simplify the factors:
(x + 6)² = 49
Square root both sides of the equation:
x + 6 = 7 x + 6 = -7
Subtract 6 from both sides of each equation:
x = 1 x - 13