Question

Solve the given quadratic equation by completing the square, $x^2+16x-9=0$

Answer 1

The given quadratic equation is $x^2+16x-9=0$.

Add and subtract $64$ in the equation $x^2+16x-9=0$ to make a perfect square as shown below:

$x^2+16x-9=0\Rightarrow x^2+16x+64-64-9=0\Rightarrow (x{)}^2+(2\times x\times 8)+8^2+(-64-9)=0\Rightarrow {(x+8)}^2-73=0(\because (a+b{)}^2=a^2+b^2+2ab)\Rightarrow {(x+8)}^2=73\Rightarrow x+8=\pm \sqrt{73}\Rightarrow x+8=-\sqrt{73},x+8=\sqrt{73}\Rightarrow x=-(\sqrt{73}+8),x=\sqrt{73}-8$

Hence, $x=-(\sqrt{73}+8)$ or $x=\sqrt{73}-8$.