Question

Complete the square. x2 + 18x + 90 = 0

Answer 1

we have the equation

`x^2+18x+90=0`

Complete the square

`\begin{gathered} (x^2+18x)+90=0 \\ (x^2+18x+9^2-9^2)+90=0 \\ (x^2+18x+9^2)+90-9^2=0 \\ (x^2+18x+81)+9=0 \end{gathered}`

Rewrite as perfect squares

`\begin{gathered} (x+9)^2+9=0 \\ (x+9)^2=-9 \end{gathered}`

take square root both sides

`√((x+9)^2)=\pm√(-9)`
`\begin{gathered} x+9=\pm3i \\ x=-9\pm3i \end{gathered}`