Question

Solve by completing the square :

$b^2+8b-4=16$

Short answer

The required value of$x$is$2,-10$

Step-by-step solution

Given information

$b^2+8b-4=16$

Calculation

$$\begin{gathered} b^2+8b-4=16 \\ \Rightarrow b^2+8b=16+4 \\ \Rightarrow b^2+8b+{(\frac{1}{2}\times 8)}^2=20+16 \\ \Rightarrow b^2+8b+16=20+16 \\ \Rightarrow {(b+4)}^2=36\Rightarrow b+4=\pm \sqrt{36}=\pm 6 \\ \Rightarrow b=-4\pm 6 \\ =-4+6,-4-6 \\ =2,-10 \end{gathered}$$

The required value of $\mathrm{x}$is $-10,2$