Chapter 9.4, Problem 26E

To determine

To solve the equation by complete the square for expression.

  $x^2+4x-21=0$

Answer to Problem 26E

The solutions are $-7$ and $3$

Explanation of Solution

Given information:

Expression

  $x^2+4x-21=0$

Calculation:

Original equation

  $x^2+4x-21=0$

Add 21 both sides

  $x^2+4x=21$

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

  $x^2+4x+4=21+4$

Factor $x^2+4x+4$

  ${(x+2)}^2=25$

On solving

  $x+2=\pm 5$

Subtract $2$ both sides

  $x=-2\pm 5$

Separating the equations

  $x=-2+5$ Or $x=-2-5$

On solving

  $x=3$ Or $x=-7$

The solutions are $-7$ and $3$