Complete the square to identify the two values that solve the following quadratic equation: x2−16x−13=4

Answer 1

To complete the square for the quadratic equation x^2 - 16x - 13 = 4, we first need to move the constant term to the other side of the equation:

x^2 - 16x - 13 - 4 = 0

Simplifying, we get:

x^2 - 16x - 17 = 0

To complete the square, we take half of the coefficient of x (-16/2 = -8) and square it (64). We add and subtract this value inside the parenthesis:

(x^2 - 16x + 64) - 17 - 64 = 0

Simplifying further:

(x - 8)^2 - 81 = 0

Now, we can solve the quadratic equation by taking the square root:

(x - 8)^2 = 81

Taking the square root of both sides, we get:

x - 8 = ±√81

x - 8 = ±9

Adding 8 to both sides:

x = 8 ±9

Therefore, the two values that solve the quadratic equation x^2 - 16x - 13 = 4 are x = 17 and x = -1.