Question

Solve quadratic equations of the form $x^2+bx+c=0$by completing the square.

In the following exercises , solve by completing the square.

$(y+9)(y+7)=80$

Short answer

The required value of$y$is$1,-17$

Step-by-step solution

Given information

$(y+9)(y+7)=80$

Calculation

$$\begin{gathered} (y+9)(y+7)=80 \\ \Rightarrow y(y+7)+9(y+7)=80 \\ \Rightarrow y^2+7y+9y+63=80 \\ \Rightarrow y^2+16y=80-63 \\ \Rightarrow y^2+16y=17 \\ \Rightarrow y^2+16y+{(\frac{1}{2}\times 16)}^2=17\Rightarrow y^2+16y+64=17+64 \\ \Rightarrow {(y+8)}^2=81\Rightarrow y+8=\pm \sqrt{81}=\pm 9 \\ \Rightarrow y=-8\pm 9 \\ =-8+9,-8-9 \\ =1,-17 \end{gathered}$$

The required value of$y$is$1,-17$