Question

Use completing the square to solve (x-12)(x+4)=9 for x

Answer 1

X= 4 + $\sqrt{73}$

x= 4 - $\sqrt{73}$

Answer 2

we have

$(x-12)(x+4)=9\\ x^{2} +4x-12x-48=9\\ x^{2} -8x-48=9$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2} -8x=9+48\\ x^{2} -8x=57$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2} -8x+16=57+16\\ x^{2} -8x+16=73$

Rewrite as perfect squares

$x^{2} -8x+16=73\\ (x-4)^{2} =73\\ (x-4)=(+/-)\sqrt{73}$

$x1=4+\sqrt{73} \\ x2=4-\sqrt{73}$

therefore

the answer is

$x1=4+\sqrt{73} \\ x2=4-\sqrt{73}$