Solve for x square root of x-2 = square root of 3x+5

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

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Rewrite ${\sqrt{3 x + 5}}^{2}$ as $3 x + 5$ .

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x - 2 = 3 x + 5$

Solve for $x$ .

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

Subtract $3 x$ from both sides of the equation.

$x - 2 - 3 x = 5$

Subtract $3 x$ from $x$ .

$- 2 x - 2 = 5$

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

Add $2$ to both sides of the equation.

$- 2 x = 5 + 2$

Add $5$ and $2$ .

$- 2 x = 7$

Divide each term in $- 2 x = 7$ by $- 2$ and simplify.

Divide each term in $- 2 x = 7$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{7}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{7}{- 2}$

Divide $x$ by $1$ .

$x = \frac{7}{- 2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

Exclude the solutions that do not make $\sqrt{x - 2} = \sqrt{3 x + 5}$ true.

$No solution$

Solve for x square root of x-2 = square root of 3x+5

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