Algebra Examples

$\sqrt{{(2 x - 5)}^{3}} - 10 = 17$

Step 1

Add $10$ to both sides of the equation.

$\sqrt{{(2 x - 5)}^{3}} = 17 + 10$

Step 2

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

${\sqrt{{(2 x - 5)}^{3}}}^{2} = {(17 + 10)}^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

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

${({(2 x - 5)}^{\frac{3}{2}})}^{2} = {(17 + 10)}^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

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

Tap for more steps...

Step 3.2.1.1

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

${(2 x - 5)}^{\frac{3}{2} \cdot 2} = {(17 + 10)}^{2}$

Step 3.2.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.2.1

Cancel the common factor.

${(2 x - 5)}^{\frac{3}{2} \cdot 2} = {(17 + 10)}^{2}$

Step 3.2.1.2.2

Rewrite the expression.

${(2 x - 5)}^{3} = {(17 + 10)}^{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Simplify ${(17 + 10)}^{2}$ .

Tap for more steps...

Step 3.3.1.1

Add $17$ and $10$ .

${(2 x - 5)}^{3} = 27^{2}$

Step 3.3.1.2

Raise $27$ to the power of $2$ .

${(2 x - 5)}^{3} = 729$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

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

$2 x - 5 = \sqrt[3]{729}$

Step 4.2

Simplify $\sqrt[3]{729}$ .

Tap for more steps...

Step 4.2.1

Rewrite $729$ as $9^{3}$ .

$2 x - 5 = \sqrt[3]{9^{3}}$

Step 4.2.2

Pull terms out from under the radical, assuming real numbers.

$2 x - 5 = 9$

Step 4.3

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

Tap for more steps...

Step 4.3.1

Add $5$ to both sides of the equation.

$2 x = 9 + 5$

Step 4.3.2

Add $9$ and $5$ .

$2 x = 14$

Step 4.4

Divide each term in $2 x = 14$ by $2$ and simplify.

Tap for more steps...

Step 4.4.1

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Step 4.4.2

Simplify the left side.

Tap for more steps...

Step 4.4.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.4.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Step 4.4.3

Simplify the right side.

Tap for more steps...

Step 4.4.3.1

Divide $14$ by $2$ .

$x = 7$