Solve for x 4(2x-5)^(1/3)+17=37

$4 {(2 x - 5)}^{\frac{1}{3}} + 17 = 37$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $17$ from both sides of the equation.

$4 {(2 x - 5)}^{\frac{1}{3}} = 37 - 17$

Subtract $17$ from $37$ .

$4 {(2 x - 5)}^{\frac{1}{3}} = 20$

Step 2

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${(4 {(2 x - 5)}^{\frac{1}{3}})}^{3} = 20^{3}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${(4 {(2 x - 5)}^{\frac{1}{3}})}^{3}$ .

Apply the product rule to $4 {(2 x - 5)}^{\frac{1}{3}}$ .

$4^{3} {({(2 x - 5)}^{\frac{1}{3}})}^{3} = 20^{3}$

Raise $4$ to the power of $3$ .

$64 {({(2 x - 5)}^{\frac{1}{3}})}^{3} = 20^{3}$

Multiply the exponents in ${({(2 x - 5)}^{\frac{1}{3}})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$64 {(2 x - 5)}^{\frac{1}{3} \cdot 3} = 20^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$64 {(2 x - 5)}^{\frac{1}{3} \cdot 3} = 20^{3}$

Rewrite the expression.

$64 {(2 x - 5)}^{1} = 20^{3}$

Simplify.

$64 (2 x - 5) = 20^{3}$

Apply the distributive property.

$64 (2 x) + 64 \cdot - 5 = 20^{3}$

Multiply.

Multiply $2$ by $64$ .

$128 x + 64 \cdot - 5 = 20^{3}$

Multiply $64$ by $- 5$ .

$128 x - 320 = 20^{3}$

Simplify the right side.

Raise $20$ to the power of $3$ .

$128 x - 320 = 8000$

Step 4

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Add $320$ to both sides of the equation.

$128 x = 8000 + 320$

Add $8000$ and $320$ .

$128 x = 8320$

Divide each term in $128 x = 8320$ by $128$ and simplify.

Divide each term in $128 x = 8320$ by $128$ .

$\frac{128 x}{128} = \frac{8320}{128}$

Simplify the left side.

Cancel the common factor of $128$ .

Cancel the common factor.

$\frac{128 x}{128} = \frac{8320}{128}$

Divide $x$ by $1$ .

$x = \frac{8320}{128}$

Simplify the right side.

Divide $8320$ by $128$ .

$x = 65$

Solve for x 4(2x-5)^(1/3)+17=37

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