Solve the equation for all values of x by completing the square.x, squared, minus, 8, x, equals, 3x 2 −8x=3

The given equation is x^2 - 8x = 3.

Step 1: Rearrange the equation to have all terms on one side. This gives us x^2 - 8x - 3 = 0.

Step 2: To complete the square, we need to add and subtract (b/2)^2 to the equation. Here, b is the coefficient of x, which is -8. So, (b/2)^2 = (-8/2)^2 = 16.

Step 3: Rewrite the equation as: (x^2 - 8x + 16) - 16 - 3 = 0.

Step 4: The expression in the brackets is a perfect square, so we can write it as (x - 4)^2. This gives us (x - 4)^2 - 19 = 0.

Step 5: Solve for x by taking the square root of both sides: x - 4 = ± sqrt(19), which gives x = 4 ± sqrt(19).

So, the solutions to the equation are x = 4 + sqrt(19) and x = 4 - sqrt(19).