Solve for x (3x+2)^4=232

${(3 x + 2)}^{4} = 232$

Step 1

Take the 4th root of both sides of the equation to eliminate the exponent on the left side.

$3 x + 2 = \pm \sqrt[4]{232}$

Step 2

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.

$3 x + 2 = \sqrt[4]{232}$

Subtract $2$ from both sides of the equation.

$3 x = \sqrt[4]{232} - 2$

Divide each term in $3 x = \sqrt[4]{232} - 2$ by $3$ and simplify.

Divide each term in $3 x = \sqrt[4]{232} - 2$ by $3$ .

$\frac{3 x}{3} = \frac{\sqrt[4]{232}}{3} + \frac{- 2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{\sqrt[4]{232}}{3} + \frac{- 2}{3}$

Divide $x$ by $1$ .

$x = \frac{\sqrt[4]{232}}{3} + \frac{- 2}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{\sqrt[4]{232}}{3} - \frac{2}{3}$

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

$3 x + 2 = - \sqrt[4]{232}$

Subtract $2$ from both sides of the equation.

$3 x = - \sqrt[4]{232} - 2$

Divide each term in $3 x = - \sqrt[4]{232} - 2$ by $3$ and simplify.

Divide each term in $3 x = - \sqrt[4]{232} - 2$ by $3$ .

$\frac{3 x}{3} = \frac{- \sqrt[4]{232}}{3} + \frac{- 2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- \sqrt[4]{232}}{3} + \frac{- 2}{3}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt[4]{232}}{3} + \frac{- 2}{3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{\sqrt[4]{232}}{3} + \frac{- 2}{3}$

Move the negative in front of the fraction.

$x = - \frac{\sqrt[4]{232}}{3} - \frac{2}{3}$

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

$x = \frac{\sqrt[4]{232}}{3} - \frac{2}{3}, - \frac{\sqrt[4]{232}}{3} - \frac{2}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt[4]{232}}{3} - \frac{2}{3}, - \frac{\sqrt[4]{232}}{3} - \frac{2}{3}$

Decimal Form:

$x = 0.63425378 \dots, - 1.96758711 \dots$

Solve for x (3x+2)^4=232

Related Questions

Support LCMGCF.com by disabling your adblocker.