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How do you solve $5^{3} \sqrt{4 x - 2} = 17$ $5^3 sqrt(4x - 2) = 17$ ?

3 Answers

Sep 30, 2017

$x = 0.504624$ $x = 0.504624$

Explanation:

Square both sides to get rid of the square root.

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

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

$15625 (4 x - 2) = 289 \leftarrow$ $15625 (4x-2) = 289" "larr$ isolate the bracket with $x$ $x$

$\times \times \times \times \times \times \times \times \times \times$ $color(white)(xxxxxxxxxxxxxxxxxxxx)$ Divide both sides by $15625$ $15625$

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

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

$4 x = 2.018496 \leftarrow \div 4$ $4x = 2.018496" "larr div 4$ to isolate $x$ $x$

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

$x = 0.504624$ $x = 0.504624$

Sep 30, 2017

If the intended equation was:

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

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

Explanation:

Suppose the intended equation was:

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

We can cube both sides to get:

$125 (4 x - 2) = 4913$ $125(4x-2) = 4913$

which multiplies out to get:

$500 x - 250 = 4913$ $500x-250 = 4913$

Add $250$ $250$ to both sides to get:

$500 x = 5163$ $500x = 5163$

Divide both sides by $500$ $500$ to get:

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

Sep 30, 2017

$x = 0.504624$ $color(magenta)(x=0.504624$

Explanation:

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

$:.sqrt(4x-2)=17/125$

Square both sides

$:.(sqrt(4x-2))^2=(17/125)^2$

$:.(sqrt(4x-2))^2=(0.136)^2$

$:.sqrtaxxsqrta=a$

$:.4x-2=0.018496$

$:.4x=2.018496$

$:.x=2.018496/4$

$:.color(magenta)(x=0.504624$

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

check:-

substitute $color(magenta)(x=0.504624$

$:.5^3sqrt(4(color(magenta)0.504624)-2)=17$

$:.125sqrt(0.018496)=17$

$:.125xx0.136=17$

$:.color(magenta)(17=17$

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