Chapter 11.2, Problem 27E

To determine

To calculate:

The equation by completing square

  $x^2-10x-4=0$

Answer to Problem 27E

The equation by completing square of $x^2-10x-4=0$ is $x=5\pm \sqrt{29}$ .

Explanation of Solution

Given information:

  $x^2-10x-4=0$

Calculation:

The given equation is:

  $x^2-10x-4=0$

Comparing with the standard equation of $a{x}^2+bx+c=0$ :

  $\begin{array}{l}a=1\\ b=-10\\ c=-4\end{array}$

Complete the Square ${\left(\frac{b}{2}\right)}^2$ to both the sides:

  ${\left(\frac{b}{2}\right)}^2={\left(\frac{-10}{2}\right)}^2=25$

So,

  $x^2-10x-4+25=25$

Rearrange the equation:

  $x^2-10x+25=25+4$

Factor and then simplify:

  ${\left(x-5\right)}^2=29$

Taking square root to both the sides:

  $\sqrt{{\left(x-5\right)}^2}=\pm \sqrt{29}$

Simplify:

  $x-5=\pm \sqrt{29}$

Then:

  $x=5\pm \sqrt{29}$