Solve by Factoring square root of x = square root of 3x-4

$\sqrt{x} = \sqrt{3 x - 4}$

Step 1

Subtract $\sqrt{3 x - 4}$ from both sides of the equation.

$\sqrt{x} - \sqrt{3 x - 4} = 0$

Step 2

Add $\sqrt{3 x - 4}$ to both sides of the equation.

$\sqrt{x} = \sqrt{3 x - 4}$

Step 3

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

${\sqrt{x}}^{2} = {\sqrt{3 x - 4}}^{2}$

Step 4

Simplify each side of the equation.

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

${(x^{\frac{1}{2}})}^{2} = {\sqrt{3 x - 4}}^{2}$

Simplify the left side.

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

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

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

$x^{\frac{1}{2} \cdot 2} = {\sqrt{3 x - 4}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = {\sqrt{3 x - 4}}^{2}$

Rewrite the expression.

$x^{1} = {\sqrt{3 x - 4}}^{2}$

Simplify.

$x = {\sqrt{3 x - 4}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{3 x - 4}}^{2}$ as $3 x - 4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 4}$ as ${(3 x - 4)}^{\frac{1}{2}}$ .

$x = {({(3 x - 4)}^{\frac{1}{2}})}^{2}$

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

$x = {(3 x - 4)}^{\frac{1}{2} \cdot 2}$

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

$x = {(3 x - 4)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = {(3 x - 4)}^{\frac{2}{2}}$

Rewrite the expression.

$x = {(3 x - 4)}^{1}$

Simplify.

$x = 3 x - 4$

Step 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.

$x - 3 x = - 4$

Subtract $3 x$ from $x$ .

$- 2 x = - 4$

Divide each term in $- 2 x = - 4$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 4$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 2}$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$x = 2$

Solve by Factoring square root of x = square root of 3x-4

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