# Can someone solve this by either factoring, graphing, quadratic formula, or completing the square? The problem is 3x^2+7x-24=13x

Oct 12, 2017

$x = 4 \text{ }$ and $\text{ } x = - 2$

#### Explanation:

I'll solve by completing the square.

First, subtract $13 x$ from both sides:

$3 {x}^{2} + 7 x - 24 = 13 x$

$3 {x}^{2} - 6 x - 24 = 0$

Next, divide both sides by $3$

${x}^{2} - 2 x - 8 = 0$

We need something of the form ${x}^{2} + 2 a x + {a}^{2}$.
Notice that our $2 a$ is $- 2$, so we know $a = - 1$ and therefore ${a}^{2} = 1$.

To get a perfect square, we can split $- 8$ into $+ 1 - 9$.

${x}^{2} - 2 x + 1 - 9 = 0$

$\left({x}^{2} - 2 x + 1\right) - 9 = 0$

${\left(x - 1\right)}^{2} - 9 = 0$

Now, move the 9 to the other side, take the square root of both sides, and solve for $x$.

${\left(x - 1\right)}^{2} = 9$

$x - 1 = \pm 3$

$x = 1 \pm 3$

So now we have our two solutions; the only thing left to do is separate them:

$x = 1 + 3 \text{ }$ and $\text{ } x = 1 - 3$

$x = 4 \text{ }$ and $\text{ } x = - 2$