Solve the equation for all values of x by completing the square.x, squared, minus, 40, equals, minus, 6, xx 2 −40=−6x

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 + 6x - 40 = 0.

2. Now, we need to complete the square. To do this, we take the coefficient of the x term (which is 6), divide it by 2, and square it. This gives us (6/2)^2 = 9.

3. We add this number to both sides of the equation to complete the square: x^2 + 6x + 9 = 40 + 9.

4. This simplifies to: (x + 3)^2 = 49.

5. Now, we take the square root of both sides. Remember, when we take the square root of a number, we get two solutions: one positive and one negative. So, x + 3 = ±√49.

6. This simplifies to: x + 3 = ±7.

7. Finally, we subtract 3 from both sides to solve for x: x = -3 ± 7.

So, the solutions to the equation are x = 4 and x = -10.