Chapter 9.4, Problem 20E

To determine

To solve the equation by complete the square for expression.

  $x^2+2x=5$

Answer to Problem 20E

The solutions are $-1+\sqrt{6}$ and $-1-\sqrt{6}$

Explanation of Solution

Given information:

Expression

  $x^2+2x=5$

Calculation:

Original equation

  $x^2+2x=5$

Since ${\left(\frac{2}{2}\right)}^2=1$ , add 1 to both sides

  $x^2+2x+1=5+1$

Factor $x^2+2x+1$

  ${(x+1)}^2=6$

On solving

  $x+1=\pm \sqrt{6}$

Subtract 1 both sides

  $x=-1\pm \sqrt{6}$

Separating the equations

  $x=-1+\sqrt{6}$ Or $x=-1-\sqrt{6}$

The solutions are $-1+\sqrt{6}$ and $-1-\sqrt{6}$