Question

solve the equation ( x^2 - 8x - 6 = 0 ) by completing the square and fill in the boxes below with the exact solution values.
(for example, if your solutions turned out to be ( -37 pm sqrt{71} ), you would type -37 in input box 1 and 71 in input box 2).
( x = ) (\boxed{\text{input box 1}}) ( pm sqrt{\boxed{\text{input box 2}}} )

Explanation:

Step1: Move the constant term

Start with the equation \(x^2 - 8x - 6 = 0\). Add 6 to both sides to get \(x^2 - 8x = 6\).

Step2: Complete the square

Take half of the coefficient of \(x\), which is \(\frac{-8}{2} = -4\), square it: \((-4)^2 = 16\). Add 16 to both sides: \(x^2 - 8x + 16 = 6 + 16\).

Step3: Factor and simplify

The left side factors as \((x - 4)^2\), and the right side is \(22\). So \((x - 4)^2 = 22\). Take the square root of both sides: \(x - 4 = \pm\sqrt{22}\). Then add 4 to both sides: \(x = 4 \pm\sqrt{22}\).

Answer:

Input Box 1: 4
Input Box 2: 22