# How do you factor and solve  x^2-12x=-6 ?

Apr 29, 2017

Bring over the $- 6$ and factor as you would a simple trinomial.

In this case, that doesn't work (it's "unfactorable"), and you have to use the quadratic formula to solve.

As a result, you'll get $x \cong 11.477$ and $x \cong 0.523$.

#### Explanation:

Factoring

In order to factor, let's first bring the $- 6$ over, and equate the equation to $0$.

${x}^{2} - 12 x = - 6$

${x}^{2} - 12 x + 6 = 0$

Now, let's factor it as you would a simple trinomial. Meaning, "what two numbers multiplied equals $a c$ and added equals $b$?"

There are no numbers that fits this requirement (^). Therefore, it is "unfactorable". Due to this, we have to use the second way to factor: quadratic equation.

This ultimately brings us to...

Solving.

$x = \setminus \frac{- b \setminus \pm \setminus \sqrt{{b}^{2} - 4 a c \setminus}}{2 a}$

Now let's sub in the values.

$x = \setminus \frac{- \left(- 12\right) \setminus \pm \setminus \sqrt{{\left(- 12\right)}^{2} - 4 \left(1\right) \left(6\right) \setminus}}{2 \left(1\right)}$

$x = \setminus \frac{12 \setminus \pm \setminus \sqrt{120 \setminus}}{2}$

At this point, we can solve for $x$. We will get two answers because of the $\pm$ sign.

$x = \setminus \frac{12 \setminus \pm \setminus \sqrt{120 \setminus}}{2}$

1. $x = \setminus \frac{12 \setminus + \setminus \sqrt{120}}{2}$

$x \cong \setminus \frac{22.954}{2}$

$x \cong 11.477$

2.
$x = \setminus \frac{12 \setminus - \setminus \sqrt{120}}{2}$

$x \cong \setminus \frac{1.046}{2}$

$x \cong 0.523$

We can graph the equation to check our work.

graph{x^2 - 12x + 6 [-2.8, 22.51, -6.33, 6.33]}

As you can see, the zeros match up.

Hope this helps :)