Question

What is the intermediate step in the form (x + a)2 = b as a result of completing the square for the following equation? x^2 – 18x = -117

Answer 1

Divide the coefficient of the second term by 2, and then square it to get the third term:

`(18)/(2)\rightarrow9\rightarrow81`

Then, add 81 (the intermediate step) to both sides:

`x^2-18x+81=-117+81`

Factor and simplify:

`\begin{gathered} x^2-18x+81=-117+81 \\ \Rightarrow(x-9)^2=-36 \end{gathered}`