Solve for x -2 cube root of 2x+5+7=15

$- 2 \sqrt[3]{2 x + 5} + 7 = 15$

Step 1

Move all terms not containing $- 2 \sqrt[3]{2 x + 5}$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$- 2 \sqrt[3]{2 x + 5} = 15 - 7$

Subtract $7$ from $15$ .

$- 2 \sqrt[3]{2 x + 5} = 8$

Step 2

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

${(- 2 \sqrt[3]{2 x + 5})}^{3} = 8^{3}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x + 5}$ as ${(2 x + 5)}^{\frac{1}{3}}$ .

${(- 2 {(2 x + 5)}^{\frac{1}{3}})}^{3} = 8^{3}$

Simplify the left side.

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

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

${(- 2)}^{3} {({(2 x + 5)}^{\frac{1}{3}})}^{3} = 8^{3}$

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

$- 8 {({(2 x + 5)}^{\frac{1}{3}})}^{3} = 8^{3}$

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

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

$- 8 {(2 x + 5)}^{\frac{1}{3} \cdot 3} = 8^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 8 {(2 x + 5)}^{\frac{1}{3} \cdot 3} = 8^{3}$

Rewrite the expression.

$- 8 {(2 x + 5)}^{1} = 8^{3}$

Simplify.

$- 8 (2 x + 5) = 8^{3}$

Apply the distributive property.

$- 8 (2 x) - 8 \cdot 5 = 8^{3}$

Multiply.

Multiply $2$ by $- 8$ .

$- 16 x - 8 \cdot 5 = 8^{3}$

Multiply $- 8$ by $5$ .

$- 16 x - 40 = 8^{3}$

Simplify the right side.

Raise $8$ to the power of $3$ .

$- 16 x - 40 = 512$

Step 4

Solve for $x$ .

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

Add $40$ to both sides of the equation.

$- 16 x = 512 + 40$

Add $512$ and $40$ .

$- 16 x = 552$

Divide each term in $- 16 x = 552$ by $- 16$ and simplify.

Divide each term in $- 16 x = 552$ by $- 16$ .

$\frac{- 16 x}{- 16} = \frac{552}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 x}{- 16} = \frac{552}{- 16}$

Divide $x$ by $1$ .

$x = \frac{552}{- 16}$

Simplify the right side.

Cancel the common factor of $552$ and $- 16$ .

Factor $8$ out of $552$ .

$x = \frac{8 (69)}{- 16}$

Cancel the common factors.

Factor $8$ out of $- 16$ .

$x = \frac{8 \cdot 69}{8 \cdot - 2}$

Cancel the common factor.

$x = \frac{8 \cdot 69}{8 \cdot - 2}$

Rewrite the expression.

$x = \frac{69}{- 2}$

Move the negative in front of the fraction.

$x = - \frac{69}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{69}{2}$

Decimal Form:

$x = - 34.5$

Mixed Number Form:

$x = - 34 \frac{1}{2}$

Solve for x -2 cube root of 2x+5+7=15

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