Complete the square to identify the two values that solve the following quadratic equation: x2−16x−13=4 .(1 point)
Starting with the equation x^2 - 16x - 13 = 4, we want to complete the square by adding and subtracting the necessary term to both sides to create a perfect square trinomial.
To complete the square, we need to add (16/2)^2 = 64 to both sides:
x^2 - 16x + 64 - 13 = 4 + 64
Simplifying:
(x - 8)^2 - 13 = 68
Next, we isolate (x - 8)^2 by adding 13 to both sides:
(x - 8)^2 = 81
Taking the square root of both sides:
x - 8 = ±9
Adding 8 to both sides gives us the solutions:
x = 8 ± 9
The two values that solve the quadratic equation x^2 - 16x - 13 = 4 are:
x = 17 and x = -1