# How do you solve 22x-x^2=96?

Mar 15, 2018

$x = 16 \mathmr{and} 6$

#### Explanation:

$22 x - {x}^{2} = 96$

$- {x}^{2} + 22 x - 96 = 0$

${x}^{2} - 22 x + 96 = 0$

$\left(x - 16\right) \left(x - 6\right) = 0$

Hence, $x = 16 \mathmr{and} 6$

Mar 15, 2018

$x = 6 \mathmr{and} 16$

#### Explanation:

So first we want to get the ${x}^{2}$ to be positive. To do this we have to multiply both sides by a $\left(- 1\right)$.
$\left(- 1\right) \left[22 x - {x}^{2} = 96\right]$

Giving us
$- 22 x + {x}^{2} = - 96$

Now we can get all numbers to one side of the equation making it equal to $0$.
${x}^{2} - 22 x + 96 = 0$

Now we can factor. Since $- 16 \cdot - 6 = 96$
We can now write ${x}^{2} - 22 x + 96$

As
$\left(x - 16\right) \left(x - 6\right) = 0$

Setting both to $0$ gives us
$x - 16 = 0$ and $x - 6 = 0$

Which gives us
$x = 16$ and $x = 6$