Chapter 9.4, Problem 18E

To determine

To solve the equation by complete the square for expression.

  $x^2-6x=16$

Answer to Problem 18E

The solutions are 8 and -2

Explanation of Solution

Given information:

Expression

  $x^2-6x=16$

Calculation:

Original equation

  $x^2-6x=16$

Since ${\left(\frac{-6}{2}\right)}^2=9$ , add 9 to both sides

  $x^2-6x+9=16+9$

Factor $x^2-6x+9$

  ${(x-3)}^2=25$

On solving

  $x-3=\pm 5$

Add 3 both sides

  $x=3\pm 5$

Separating the equations

  $x=3+5$ Or $x=3-5$

  $x=8$ Or $x=-2$

The solutions are 8 and -2