Question

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

Answer 1

x= 4 +
`√(73)`

x= 4 -
`√(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)=(+/-)√(73)`

`x1=4+√(73) \\ x2=4-√(73)`

therefore

the answer is

`x1=4+√(73) \\ x2=4-√(73)`