Solve the equation for all values of x by completing the square.x, squared, plus, 20, x, plus, 86, equals, 0x 2 +20x+86=0

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

1. First, we have the equation x^2 + 20x + 86 = 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, (20/2)^2 = 100.

3. Rewrite the equation, adding and subtracting this number: x^2 + 20x + 100 - 100 + 86 = 0.

4. This simplifies to (x + 10)^2 - 14 = 0.

5. Now, solve for x by first adding 14 to both sides to get (x + 10)^2 = 14.

6. Then, take the square root of both sides. Remember to consider both the positive and negative roots. This gives us x + 10 = sqrt(14) and x + 10 = -sqrt(14).

7. Finally, subtract 10 from both sides to solve for x. This gives us x = -10 + sqrt(14) and x = -10 - sqrt(14).

So, the solutions to the equation are x = -10 + sqrt(14) and x = -10 - sqrt(14).