Solve for x 5(2x-1)^(2/3)=125

$5 {(2 x - 1)}^{\frac{2}{3}} = 125$

Step 1

Divide each term in $5 {(2 x - 1)}^{\frac{2}{3}} = 125$ by $5$ and simplify.

Divide each term in $5 {(2 x - 1)}^{\frac{2}{3}} = 125$ by $5$ .

$\frac{5 {(2 x - 1)}^{\frac{2}{3}}}{5} = \frac{125}{5}$

Simplify the left side.

Cancel the common factor.

$\frac{5 {(2 x - 1)}^{\frac{2}{3}}}{5} = \frac{125}{5}$

Divide ${(2 x - 1)}^{\frac{2}{3}}$ by $1$ .

${(2 x - 1)}^{\frac{2}{3}} = \frac{125}{5}$

Simplify the right side.

Divide $125$ by $5$ .

${(2 x - 1)}^{\frac{2}{3}} = 25$

Step 2

Raise each side of the equation to the power of $\frac{3}{2}$ to eliminate the fractional exponent on the left side.

${({(2 x - 1)}^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 25^{\frac{3}{2}}$

Step 3

Simplify the exponent.

Simplify the left side.

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

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

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

${(2 x - 1)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 25^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x - 1)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 25^{\frac{3}{2}}$

Rewrite the expression.

${(2 x - 1)}^{\frac{1}{3} \cdot 3} = \pm 25^{\frac{3}{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(2 x - 1)}^{\frac{1}{3} \cdot 3} = \pm 25^{\frac{3}{2}}$

Rewrite the expression.

${(2 x - 1)}^{1} = \pm 25^{\frac{3}{2}}$

Simplify.

$2 x - 1 = \pm 25^{\frac{3}{2}}$

Simplify the right side.

Simplify $\pm 25^{\frac{3}{2}}$ .

Simplify the expression.

Rewrite $25$ as $5^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$2 x - 1 = \pm 5^{3}$

Raise $5$ to the power of $3$ .

$2 x - 1 = \pm 125$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$2 x - 1 = 125$

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

Add $1$ to both sides of the equation.

$2 x = 125 + 1$

Add $125$ and $1$ .

$2 x = 126$

Divide each term in $2 x = 126$ by $2$ and simplify.

Divide each term in $2 x = 126$ by $2$ .

$\frac{2 x}{2} = \frac{126}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{126}{2}$

Divide $x$ by $1$ .

$x = \frac{126}{2}$

Simplify the right side.

Divide $126$ by $2$ .

$x = 63$

Next, use the negative value of the $\pm$ to find the second solution.

$2 x - 1 = - 125$

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

Add $1$ to both sides of the equation.

$2 x = - 125 + 1$

Add $- 125$ and $1$ .

$2 x = - 124$

Divide each term in $2 x = - 124$ by $2$ and simplify.

Divide each term in $2 x = - 124$ by $2$ .

$\frac{2 x}{2} = \frac{- 124}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 124}{2}$

Divide $x$ by $1$ .

$x = \frac{- 124}{2}$

Simplify the right side.

Divide $- 124$ by $2$ .

$x = - 62$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 63, - 62$

Solve for x 5(2x-1)^(2/3)=125

Related Questions

Support LCMGCF.com by disabling your adblocker.