For a quadratic of the form [tex]x^2+bx=-c[/tex], we can solve by completing the square.
First, we must expand the expression and convert it to the form above.
[tex](x-12)(x+4)=9\\x^2+4x-12x-48=9\\x^2-8x=57[/tex]
Completing the square is like forcing a quadratic to be factored like a perfect square trinomial. To do so, we add the square of half of the coefficient b, [tex]( \frac{b}{2})^2[/tex], to both sides of the equation.
[tex]x^2-8x+( \frac{-8}{2})^2=57+( \frac{-8}{2})^2\\\\x^2-8x+16=57+16[/tex]
We then factor like a perfect square trinomial and simplify.
[tex](x-4)^2=73[/tex]
[tex]x-4= \pm \sqrt{73} \\\\ x = 4+\sqrt{73} \ or \ x = 4-\sqrt{73}[/tex]
