Question

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

Answer 1

For a quadratic of the form $x^2+bx=-c$, we can solve by completing the square.

First, we must expand the expression and convert it to the form above.

$(x-12)(x+4)=9\\x^2+4x-12x-48=9\\x^2-8x=57$

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, $( \frac{b}{2})^2$, to both sides of the equation.

$x^2-8x+( \frac{-8}{2})^2=57+( \frac{-8}{2})^2\\\\x^2-8x+16=57+16$

We then factor like a perfect square trinomial and simplify.

$(x-4)^2=73$

$x-4= \pm \sqrt{73} \\\\ x = 4+\sqrt{73} \ or \ x = 4-\sqrt{73}$

Answer 2

Answer:

The correct answer is

D