Question

question solve the equation for all values of x by completing the square. express your answer in simplest form. $x^{2}-8 = 2x$

Explanation:

Step1: Rearrange the equation

$x^{2}-2x - 8=0$

Step2: Move the constant term

$x^{2}-2x=8$

Step3: Complete the square on the left - hand side

Add $(\frac{-2}{2})^2 = 1$ to both sides of the equation: $x^{2}-2x + 1=8 + 1$.
The left - hand side can be written as $(x - 1)^{2}$, so $(x - 1)^{2}=9$.

Step4: Take the square root of both sides

$x-1=\pm\sqrt{9}=\pm3$.

Step5: Solve for x

When $x - 1=3$, $x=4$; when $x - 1=-3$, $x=-2$.

Answer:

$x = 4$ or $x=-2$