Chapter 9.4, Problem 22E

To determine

To solve the equation by complete the square for expression.

  $x^2+11x=-10$

Answer to Problem 22E

The solutions are $-1$ and $-10$

Explanation of Solution

Given information:

Expression

  $x^2+11x=-10$

Calculation:

Original equation

  $x^2+11x=-10$

Since ${\left(\frac{11}{2}\right)}^2=\frac{121}{4}$ , add $\frac{121}{4}$ to both sides

  $x^2+11x+\frac{121}{4}=-10+\frac{121}{4}$

Factor $x^2+11x+\frac{121}{4}$

  $\frac{1}{4}(4x^2+44x+121)=\frac{81}{4}$

On solving

  $(4x^2+44x+121)=81$

On solving

  ${(2x+11)}^2=81$

On solving

  $2x+11=\pm 9$

Subtract $11$ both sides

  $2x=-11\pm 9$

Divide by $2$ both sides

  $x=\frac{-11\pm 9}{2}$

Separating the equations

  $x=\frac{-11+9}{2}$ Or $x=\frac{-11-9}{2}$

On solving

  $x=-1$ Or $x=-10$

The solutions are $-1$ and $-10$