Question

Solve the equation $x^2-8x-2=0$ by completing the squares.

Short answer

The solution for the given equation is $x=4\pm 3\sqrt{2}$.

Step-by-step solution

Step 1. Write down the given information.

The given equation is $x^2-8x-2=0$.

Step 2. Apply square completion method.

The given equation $x^2-8x-2=0$ with the help of completing the square method is solved as:

$\begin{array}{c}{x}^2-8x-2=0....\left(\text{Given}\right)\\ x^2-8x=2....\left(\text{Rewrite}\right)\\ x^2-8x+16=2+16....\left(\begin{array}{l}\text{Add}{\left(-\frac{8}{2}\right)}^2\\ \text{bothsides}\end{array}\right)\\ {\left(x-4\right)}^2=18\\ x-4=\pm 3\sqrt{2}\\ x=4\pm 3\sqrt{2}\end{array}$

Step 3. Conclusion.

The solution for the given equation is $x=4\pm 3\sqrt{2}$.