Chapter 9.4, Problem 21E

To determine

To solve the equation by complete the square for expression.

  $x^2-5x=8$

Answer to Problem 21E

The solutions are $\frac{5}{2}+\sqrt{57}$ and $\frac{5}{2}-\sqrt{57}$

Explanation of Solution

Given information:

Expression

  $x^2-5x=8$

Calculation:

Original equation

  $x^2-5x=8$

Since ${\left(\frac{-5}{2}\right)}^2=\frac{25}{4}$ , add $\frac{25}{4}$ to both sides

  $x^2-5x+\frac{25}{4}=8+\frac{25}{4}$

Factor $x^2-5x+\frac{25}{4}$

  $\frac{1}{4}\times \left(x^2-5x+\frac{25}{4}\right)=\frac{57}{4}$

On solving

  $\left(x^2-5x+\frac{25}{4}\right)=57$

On solving

  ${\left(x-\frac{5}{2}\right)}^2=57$

On solving

  $\left(x-\frac{5}{2}\right)=\pm \sqrt{57}$

Add $\left(\frac{5}{2}\right)$ both sides

  $x=\frac{5}{2}\pm \sqrt{57}$

Separating the equations

  $x=\frac{5}{2}+\sqrt{57}$ Or $x=\frac{5}{2}-\sqrt{57}$

The solutions are $\frac{5}{2}+\sqrt{57}$ and $\frac{5}{2}-\sqrt{57}$