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^2-7x=-9x-2

Answer 1

$\begin{gathered} x^2-7x=-9x-2 \\ \text{add (-9x-2) to both sides:} \\ x^2-7x+9x+2=0 \\ x^2+2x+2=0 \end{gathered}$

Subtract 2 from both sides:

$x^2+2x=-2$

Group terms together on the left hand side with a placeholder constant:

$(x^2+2x+_-)=_--2$

Take one half of the coefficient of x and square it, then add it to both sides:

$\begin{gathered} (\frac{2}{2})^2=1 \\ x^2+2x+1=1-2 \\ x^2+2x+1=-1 \\ \text{where:} \\ x^2+2x+1=(x+1)^2 \\ \text{therefore:} \\ (x+1)^2=-1 \end{gathered}$