# what is 16x^2 = 56x ?

Mar 27, 2018

$x = \frac{7}{2}$

#### Explanation:

Divide both sides by $x .$ This will cause $x$ to cancel out on the right hand side.

$\frac{16 {x}^{2}}{x} = \frac{56 \cancel{x}}{\cancel{x}}$

Recall that ${x}^{a} / {x}^{b} = {x}^{a - b}$

Thus, we have

$16 {x}^{2 - 1} = 56$

$16 x = 56$

Divide both sides by $16 :$

$\frac{\cancel{16} x}{\cancel{16}} = \frac{56}{16}$

Simplify:

x=56/16=color(red)(7/2

Mar 27, 2018

$x = 0$ or $x = 3 \frac{1}{2}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} 16 {x}^{2} = 56 x$

After subtracting $56 x$ from both sides:
$\textcolor{w h i t e}{\text{XXX}} 16 {x}^{2} - 56 x = 0$

Factoring out the $x$ on the left side
$\textcolor{w h i t e}{\text{XXX}} x \left(16 x - 56\right) = 0$

This implies that
{: ("either",x=0," or ",16x-56=0), (,,,rarr x=56/16=7/2=3 1/2) :}