# How do you solve x^2+10x=15?

Apr 6, 2018

$x = - 5 \pm \sqrt{30}$

Here's how I did it:

#### Explanation:

${x}^{2} + 10 x = 15$

First, we want to set one side to $0$ and let one side have $3$ terms so that we can factor it, so we subtract $15$ from both sides of the equation:
${x}^{2} + 10 x - 15 = 0$

Now we factor. We have to find two numbers that:

• Multiply up to $- 15$
• Add up to $10$.

We know that the factors of $- 15$ are $- 15 , - 5 , - 3 , - 1 , 1 , 3 , 5 ,$ and $15$. However, no group of factors of $- 15$ can add up to $10$, so we have to do another method, called the quadratic formula.

The quadratic formula is $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$.

Our equation is in the form of $a {x}^{2} + b {x}^{2} + c$, which is also called standard form. So we know that:
$a = 1$

$b = 10$

$c = - 15$

Now let's substitute these values into the quadratic formula:
$x = \frac{- 10 \pm \sqrt{{10}^{2} - 4 \left(1\right) \left(- 5\right)}}{2 \left(1\right)}$

Simplify by doing ${10}^{2}$, $- 4 \left(1\right) \left(- 5\right)$, and $2 \left(1\right)$:
$x = \frac{- 10 \pm \sqrt{100 + 20}}{2}$

Add $100 + 20$:
$x = \frac{- 10 \pm \sqrt{120}}{2}$

Radicalize/simplify $120$
$x = \frac{- 10 \pm \sqrt{4 \cdot 30}}{2}$

$x = \frac{- 10 \pm 2 \sqrt{30}}{2}$

Divide by $2$:
$x = - 5 \pm \sqrt{30}$

Hope this helps!