Question

Solve the quadratic equation by completing the square: x^2 + 16x +51 = 0

Answer 1

x = ±√13 - 8

Explanation:

Move the constant term to the right side of the equation.

x² + 16x + 51 = 0

x² + 16x = -51

We complete the square by taking half of the coefficient, squaring it, and adding it to both sides of the equation. The formula is (b/2)².

x² + 16x = -51

here the formula would be (16/2)² = 64

x² + 16x + 64 = -51 + 64

Now just simplify by factoring the left side and adding up the right side.

(x + 8)² = 13

You have to isolate x to find what it equals. Here start by taking the square root of both sides

x + 8 = √13

Subtract 8 to both sides

x = ±√13 - 8