Answer
$x=-1$ and $x=-10$
Work Step by Step
The given equation is
$\Rightarrow x^2+11x=-10$
Find the value of $(\frac{b}{2})^2$.
Substitute $11$ for $b$.
$=(\frac{11}{2})^2$
Simplify.
$=\frac{121}{4}$
Add $\frac{121}{4}$ to each side of the equation.
$\Rightarrow x^2+11x+\frac{121}{4}=-10+\frac{121}{4}$
Simplify.
$\Rightarrow x^2+11x+\frac{121}{4}=\frac{-40+121}{4}$
$\Rightarrow x^2+11x+\frac{121}{4}=\frac{81}{4}$
Write the left side as the square of a binomial.
$\Rightarrow (x+\frac{11}{2})^2=\frac{81}{4}$
Take the square root of each side.
$\Rightarrow x+\frac{11}{2}=\pm \frac{9}{2}$
Subtract $\frac{11}{2}$ from each side.
$\Rightarrow x+\frac{11}{2}-\frac{11}{2}=\pm \frac{9}{2}-\frac{11}{2}$
Simplify.
$\Rightarrow x=\pm\frac{9}{2}-\frac{11}{2}$
The solutions are $x=\frac{ 9}{2}-\frac{11}{2}=-\frac{2}{2}=-1$ and $x=-\frac{ 9}{2}-\frac{11}{2}=-\frac{20}{2}=-10$.
