Question

solve the quadratic equation by completing the square. x^2 - 8x + 5 = 0. first, choose the appropriate form and fill in the blanks with the correct numbers. then, solve the equation. simplify your answer as much as possible. if there is more than one solution, separate them with commas. form: (x + )^2 = (x - )^2 = solution: x = __

Explanation:

Step1: Rewrite the equation for completing the square

For the quadratic equation \(x^{2}-8x + 5=0\), the coefficient of \(x\) is \(-8\). Half of it is \(\frac{-8}{2}=-4\), and \((x - 4)^{2}=x^{2}-8x + 16\). So we rewrite the given equation as \(x^{2}-8x=- 5\), then add 16 to both sides: \(x^{2}-8x + 16=-5 + 16\).

Step2: Simplify the equation

We get \((x - 4)^{2}=11\).

Step3: Solve for \(x\)

Taking the square - root of both sides, we have \(x-4=\pm\sqrt{11}\). Then \(x = 4\pm\sqrt{11}\).

Answer:

\(x=4+\sqrt{11},4 - \sqrt{11}\); \((x - 4)^{2}=11\)