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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

User Meilo
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\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} ((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}

User Saurabh Agarwal
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