Solve the Rational Equation for x square root of 3x+14=2

$\sqrt{3 x} + 14 = 2$

Step 1

Move all terms not containing $\sqrt{3 x}$ to the right side of the equation.

Subtract $14$ from both sides of the equation.

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

Subtract $14$ from $2$ .

$\sqrt{3 x} = - 12$

Step 2

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

${\sqrt{3 x}}^{2} = {(- 12)}^{2}$

Step 3

Simplify each side of the equation.

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

${({(3 x)}^{\frac{1}{2}})}^{2} = {(- 12)}^{2}$

Simplify the left side.

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

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

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

${(3 x)}^{\frac{1}{2} \cdot 2} = {(- 12)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x)}^{\frac{1}{2} \cdot 2} = {(- 12)}^{2}$

Rewrite the expression.

${(3 x)}^{1} = {(- 12)}^{2}$

Simplify.

$3 x = {(- 12)}^{2}$

Simplify the right side.

Raise $- 12$ to the power of $2$ .

$3 x = 144$

Step 4

Divide each term in $3 x = 144$ by $3$ and simplify.

Divide each term in $3 x = 144$ by $3$ .

$\frac{3 x}{3} = \frac{144}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{144}{3}$

Divide $x$ by $1$ .

$x = \frac{144}{3}$

Simplify the right side.

Divide $144$ by $3$ .

$x = 48$

Step 5

Exclude the solutions that do not make $\sqrt{3 x} + 14 = 2$ true.

$No solution$