Solve the equation for all values of x by completing the square.x, squared, plus, 63, equals, 16, xx 2 +63=16x

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

1. First, let's rewrite the equation to have all terms on one side: x^2 - 16x + 63 = 0

2. Now, we need to complete the square. To do this, we take the coefficient of the x term (which is -16), divide it by 2, and square it. This gives us (-16/2)^2 = 64.

3. Add and subtract this number inside the equation: x^2 - 16x + 64 - 64 + 63 = 0

4. The first three terms now form a perfect square, so we can simplify them to (x - 8)^2. The equation becomes: (x - 8)^2 - 64 + 63 = 0

5. Simplify the constants: (x - 8)^2 - 1 = 0

6. Now, we can solve for x by first adding 1 to both sides to isolate the square: (x - 8)^2 = 1

7. Then, take the square root of both sides. Remember that the square root of a number y is both positive and negative root of y. So, we get: x - 8 = ± √1

8. Finally, add 8 to both sides to solve for x: x = 8 ± 1

So, the solutions to the equation are x = 9 and x = 7.