Q65. - Algebra 2

Question

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

Step-by-Step Solution

Answer

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

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:

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

Step 3. Conclusion.

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