Solve for x square root of 5x = square root of 9x-24

$\sqrt{5 x} = \sqrt{9 x - 24}$

Step 1

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

${\sqrt{5 x}}^{2} = {\sqrt{9 x - 24}}^{2}$

Step 2

Simplify each side of the equation.

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

${({(5 x)}^{\frac{1}{2}})}^{2} = {\sqrt{9 x - 24}}^{2}$

Simplify the left side.

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

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

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

${(5 x)}^{\frac{1}{2} \cdot 2} = {\sqrt{9 x - 24}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 x)}^{\frac{1}{2} \cdot 2} = {\sqrt{9 x - 24}}^{2}$

Rewrite the expression.

${(5 x)}^{1} = {\sqrt{9 x - 24}}^{2}$

Simplify.

$5 x = {\sqrt{9 x - 24}}^{2}$

Simplify the right side.

Simplify ${\sqrt{9 x - 24}}^{2}$ .

Factor $3$ out of $9 x - 24$ .

Factor $3$ out of $9 x$ .

$5 x = {\sqrt{3 (3 x) - 24}}^{2}$

Factor $3$ out of $- 24$ .

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

Factor $3$ out of $3 (3 x) + 3 (- 8)$ .

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

Rewrite ${\sqrt{3 (3 x - 8)}}^{2}$ as $3 (3 x - 8)$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 (3 x - 8)}$ as ${(3 (3 x - 8))}^{\frac{1}{2}}$ .

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

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

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$5 x = 3 (3 x - 8)$

Apply the distributive property.

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

Multiply.

Multiply $3$ by $3$ .

$5 x = 9 x + 3 \cdot - 8$

Multiply $3$ by $- 8$ .

$5 x = 9 x - 24$

Step 3

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $9 x$ from both sides of the equation.

$5 x - 9 x = - 24$

Subtract $9 x$ from $5 x$ .

$- 4 x = - 24$

Divide each term in $- 4 x = - 24$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 24$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 24}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 24}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 24}{- 4}$

Simplify the right side.

Divide $- 24$ by $- 4$ .

$x = 6$

Solve for x square root of 5x = square root of 9x-24

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