Solve for the roots in simplest form by completing the square:x, squared, minus, 10, x, minus, 167, equals, 0x 2 −10x−167=0

Sure, let's solve the quadratic equation step by step:

1. First, let's rewrite the equation: x^2 - 10x - 167 = 0

2. To complete the square, we need to find a number that can be added and subtracted to make the equation a perfect square trinomial. This number is found by taking half of the coefficient of x, squaring it. In this case, it's (-10/2)^2 = 25.

3. Add and subtract this number inside the equation: x^2 - 10x + 25 - 25 - 167 = 0

4. Now, the first three terms form a perfect square trinomial: (x - 5)^2 - 25 - 167 = 0

5. Simplify the equation: (x - 5)^2 = 192

6. Take the square root of both sides: x - 5 = ±sqrt(192)

7. Simplify the square root: x - 5 = ±8sqrt(3)

8. Finally, solve for x: x = 5 ± 8sqrt(3)

So, the roots of the equation are x = 5 + 8sqrt(3) and x = 5 - 8sqrt(3).