Solve for x square root of 3x-4=2 square root of x-5

$\sqrt{3 x - 4} = 2 \sqrt{x - 5}$

Step 1

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

${\sqrt{3 x - 4}}^{2} = {(2 \sqrt{x - 5})}^{2}$

Step 2

Simplify each side of the equation.

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

${({(3 x - 4)}^{\frac{1}{2}})}^{2} = {(2 \sqrt{x - 5})}^{2}$

Simplify the left side.

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

Multiply the exponents in ${({(3 x - 4)}^{\frac{1}{2}})}^{2}$ .

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

${(3 x - 4)}^{\frac{1}{2} \cdot 2} = {(2 \sqrt{x - 5})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x - 4)}^{\frac{1}{2} \cdot 2} = {(2 \sqrt{x - 5})}^{2}$

Rewrite the expression.

${(3 x - 4)}^{1} = {(2 \sqrt{x - 5})}^{2}$

Simplify.

$3 x - 4 = {(2 \sqrt{x - 5})}^{2}$

Simplify the right side.

Simplify ${(2 \sqrt{x - 5})}^{2}$ .

Simplify the expression.

Apply the product rule to $2 \sqrt{x - 5}$ .

$3 x - 4 = 2^{2} {\sqrt{x - 5}}^{2}$

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

$3 x - 4 = 4 {\sqrt{x - 5}}^{2}$

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

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

$3 x - 4 = 4 {({(x - 5)}^{\frac{1}{2}})}^{2}$

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

$3 x - 4 = 4 {(x - 5)}^{\frac{1}{2} \cdot 2}$

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

$3 x - 4 = 4 {(x - 5)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 x - 4 = 4 {(x - 5)}^{\frac{2}{2}}$

Rewrite the expression.

$3 x - 4 = 4 {(x - 5)}^{1}$

Simplify.

$3 x - 4 = 4 (x - 5)$

Apply the distributive property.

$3 x - 4 = 4 x + 4 \cdot - 5$

Multiply $4$ by $- 5$ .

$3 x - 4 = 4 x - 20$

Step 3

Solve for $x$ .

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

Subtract $4 x$ from both sides of the equation.

$3 x - 4 - 4 x = - 20$

Subtract $4 x$ from $3 x$ .

$- x - 4 = - 20$

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

Add $4$ to both sides of the equation.

$- x = - 20 + 4$

Add $- 20$ and $4$ .

$- x = - 16$

Divide each term in $- x = - 16$ by $- 1$ and simplify.

Divide each term in $- x = - 16$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 16}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 16}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 16}{- 1}$

Simplify the right side.

Divide $- 16$ by $- 1$ .

$x = 16$

Solve for x square root of 3x-4=2 square root of x-5

Related Questions

Support LCMGCF.com by disabling your adblocker.