Use completing the square to solve for x in the equation (x-12)(x+4)=9. a. x = –1 or 15 b. x = 1 or 7 c. x=4+√41 d. x=4+√73

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]