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

Question

asked Mar 23, 2023 22.9k views

1 Answer

Futal · Answer 1 · 2023-03-26T20:20:49+0000

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:

Factor and simplify:

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