Solve for x square root of 2x-6- square root of 3x-14=0

$\sqrt{2 x - 6} - \sqrt{3 x - 14} = 0$

Add $\sqrt{3 x - 14}$ to both sides of the equation.

$\sqrt{2 x - 6} = \sqrt{3 x - 14}$

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

${\sqrt{2 x - 6}}^{2} = {\sqrt{3 x - 14}}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x - 6}$ as ${(2 x - 6)}^{\frac{1}{2}}$ .

${({(2 x - 6)}^{\frac{1}{2}})}^{2} = {\sqrt{3 x - 14}}^{2}$

Simplify the left side.

Simplify ${({(2 x - 6)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 x - 6)}^{\frac{1}{2}})}^{2}$ .

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

${(2 x - 6)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 x - 14}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x - 6)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 x - 14}}^{2}$

Rewrite the expression.

${(2 x - 6)}^{1} = {\sqrt{3 x - 14}}^{2}$

Simplify.

$2 x - 6 = {\sqrt{3 x - 14}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{3 x - 14}}^{2}$ as $3 x - 14$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 14}$ as ${(3 x - 14)}^{\frac{1}{2}}$ .

$2 x - 6 = {({(3 x - 14)}^{\frac{1}{2}})}^{2}$

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

$2 x - 6 = {(3 x - 14)}^{\frac{1}{2} \cdot 2}$

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

$2 x - 6 = {(3 x - 14)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 x - 6 = {(3 x - 14)}^{\frac{2}{2}}$

Rewrite the expression.

$2 x - 6 = {(3 x - 14)}^{1}$

Simplify.

$2 x - 6 = 3 x - 14$

Solve for $x$ .

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

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

$2 x - 6 - 3 x = - 14$

Subtract $3 x$ from $2 x$ .

$- x - 6 = - 14$

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

Add $6$ to both sides of the equation.

$- x = - 14 + 6$

Add $- 14$ and $6$ .

$- x = - 8$

Divide each term in $- x = - 8$ by $- 1$ and simplify.

Divide each term in $- x = - 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 8}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 1}$

Simplify the right side.

Divide $- 8$ by $- 1$ .

$x = 8$

Solve for x square root of 2x-6- square root of 3x-14=0

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