# How do you solve 5^3 sqrt(4x - 2) = 17 ?

Sep 30, 2017

$x = 0.504624$

#### Explanation:

Square both sides to get rid of the square root.

${\left({5}^{3} \sqrt{4 x - 2}\right)}^{2} = {17}^{2}$

${5}^{6} \times \left(4 x - 2\right) = 289$

$15625 \left(4 x - 2\right) = 289 \text{ } \leftarrow$ isolate the bracket with $x$

$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times \times \times}$Divide both sides by $15625$

$4 x - 2 = \frac{289}{15625} \text{ } \leftarrow$ isolate the term in $x$

$4 x = \frac{289}{15625} + 2$

$4 x = 2.018496 \text{ } \leftarrow \div 4$ to isolate $x$

$x = \frac{2.018496}{4}$

$x = 0.504624$

Sep 30, 2017

If the intended equation was:

$5 \sqrt[3]{4 x - 2} = 17$

then $x = \frac{5163}{500} = 10.326$

#### Explanation:

Suppose the intended equation was:

$5 \sqrt[3]{4 x - 2} = 17$

We can cube both sides to get:

$125 \left(4 x - 2\right) = 4913$

which multiplies out to get:

$500 x - 250 = 4913$

Add $250$ to both sides to get:

$500 x = 5163$

Divide both sides by $500$ to get:

$x = \frac{5163}{500} = 10.326$

Sep 30, 2017

color(magenta)(x=0.504624

#### Explanation:

${5}^{3} \sqrt{4 x - 2} = 17$

$\therefore \sqrt{4 x - 2} = \frac{17}{125}$

Square both sides

$\therefore {\left(\sqrt{4 x - 2}\right)}^{2} = {\left(\frac{17}{125}\right)}^{2}$

$\therefore {\left(\sqrt{4 x - 2}\right)}^{2} = {\left(0.136\right)}^{2}$

$\therefore \sqrt{a} \times \sqrt{a} = a$

$\therefore 4 x - 2 = 0.018496$

$\therefore 4 x = 2.018496$

$\therefore x = \frac{2.018496}{4}$

:.color(magenta)(x=0.504624

~~~~~~~~~~~~~~~~~

check:-

substitute color(magenta)(x=0.504624

$\therefore {5}^{3} \sqrt{4 \left(\textcolor{m a \ge n t a}{0.504624}\right) - 2} = 17$

$\therefore 125 \sqrt{0.018496} = 17$

$\therefore 125 \times 0.136 = 17$

:.color(magenta)(17=17