Complete the square to identify the two values that solve the following quadratic equation: x^2−16x−13=4
.(1 point)
x=
To complete the square, we want to rearrange the equation so that it is in the form (x-a)^2 = b.
To start, let's move the constant term to the right side:
x^2 - 16x - 13 - 4 = 0
Simplifying,
x^2 - 16x - 17 = 0
Now, we need to add a term to both sides of the equation to complete the square. To determine this term, we take half of the coefficient of x and square it. Half of -16 is -8, and (-8)^2 is 64.
x^2 - 16x + 64 - 17 = 64
Next, we can simplify the left side of the equation by factoring the trinomial:
(x - 8)^2 - 17 = 64
Now, let's isolate the squared term:
(x - 8)^2 = 64 + 17
(x - 8)^2 = 81
Taking the square root of both sides,
x - 8 = ±√81
x - 8 = ±9
Finally, solving for x:
x = 8 ± 9
The two values that solve the quadratic equation x^2 - 16x - 13 = 4 are:
x = 8 + 9 = 17
x = 8 - 9 = -1