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