Evaluate 2 cube root of x-3+15=10

$2 \sqrt[3]{x - 3} + 15 = 10$

Step 1

Move all terms not containing $2 \sqrt[3]{x - 3}$ to the right side of the equation.

Subtract $15$ from both sides of the equation.

$2 \sqrt[3]{x - 3} = 10 - 15$

Subtract $15$ from $10$ .

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

Step 2

To remove the radical on the left side of the equation, cube both sides of the equation.

${(2 \sqrt[3]{x - 3})}^{3} = {(- 5)}^{3}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x - 3}$ as ${(x - 3)}^{\frac{1}{3}}$ .

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

Simplify the left side.

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

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

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

Raise $2$ to the power of $3$ .

$8 {({(x - 3)}^{\frac{1}{3}})}^{3} = {(- 5)}^{3}$

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

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

$8 {(x - 3)}^{\frac{1}{3} \cdot 3} = {(- 5)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$8 {(x - 3)}^{\frac{1}{3} \cdot 3} = {(- 5)}^{3}$

Rewrite the expression.

$8 {(x - 3)}^{1} = {(- 5)}^{3}$

Simplify.

$8 (x - 3) = {(- 5)}^{3}$

Apply the distributive property.

$8 x + 8 \cdot - 3 = {(- 5)}^{3}$

Multiply $8$ by $- 3$ .

$8 x - 24 = {(- 5)}^{3}$

Simplify the right side.

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

$8 x - 24 = - 125$

Step 4

Solve for $x$ .

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

Add $24$ to both sides of the equation.

$8 x = - 125 + 24$

Add $- 125$ and $24$ .

$8 x = - 101$

Divide each term in $8 x = - 101$ by $8$ and simplify.

Divide each term in $8 x = - 101$ by $8$ .

$\frac{8 x}{8} = \frac{- 101}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 101}{8}$

Divide $x$ by $1$ .

$x = \frac{- 101}{8}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{101}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{101}{8}$

Decimal Form:

$x = - 12.625$

Mixed Number Form:

$x = - 12 \frac{5}{8}$

Evaluate 2 cube root of x-3+15=10

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