Question

Complete the square rational only:Solve the equation for all values of x by completing the square.x^2 – 27 = –6x

Answer 1

`\begin{gathered} x^2-27=-6x \\ \text{add 27 to both sides} \\ x^2-27+27=-6x+27 \\ x^2=-6x+27 \\ add\text{ 6x to both sides} \\ x^2+6x=-6x+6x+27 \\ x^2+6x=27 \\ x^2+6x+3^2=27+3^2 \\ x^2+6x+9=36 \\ (x+3)^2=36 \\ x+3=6 \\ x=6-3 \\ x=3 \\ Note\text{ }\sqrt[]{36}\text{ can be -6} \\ x+3=-6 \\ x=-6-3 \\ x=-9 \\ x=3\text{ and x=-9} \end{gathered}`