Question

In the following exercise, solve by completing the square.

$z^2+12z=-11$

Short answer

The required solution is$z=-1$.

Step-by-step solution

Step 1. Given Information

We are given the quadratic equation

$z^2+12z=-11$

Step 2. Calculation

$z^2+12z=-11$

$\Rightarrow z^2+12z+{\left(\frac{12}{2}\right)}^2=-11+{\left(\frac{12}{2}\right)}^2$ take half of $12$, square it and add it to both sides

$\Rightarrow z^2+12z+36=-11+36$

$\Rightarrow z^2+12z+36=25$ simplify

$\Rightarrow {(z+6)}^2=25$ write it as binomial squared

$\Rightarrow z+6=5$ take square root on each side

$\Rightarrow z=-1$ simplify