Solve the Rational Equation for x 2 = square root of 3x+34

$2 = \sqrt{3 x + 34}$

Rewrite the equation as $\sqrt{3 x + 34} = 2$ .

$\sqrt{3 x + 34} = 2$

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

${\sqrt{3 x + 34}}^{2} = 2^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x + 34}$ as ${(3 x + 34)}^{\frac{1}{2}}$ .

${({(3 x + 34)}^{\frac{1}{2}})}^{2} = 2^{2}$

Simplify the left side.

Simplify ${({(3 x + 34)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x + 34)}^{\frac{1}{2}})}^{2}$ .

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

${(3 x + 34)}^{\frac{1}{2} \cdot 2} = 2^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x + 34)}^{\frac{1}{2} \cdot 2} = 2^{2}$

Rewrite the expression.

${(3 x + 34)}^{1} = 2^{2}$

Simplify.

$3 x + 34 = 2^{2}$

Simplify the right side.

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

$3 x + 34 = 4$

Solve for $x$ .

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

Subtract $34$ from both sides of the equation.

$3 x = 4 - 34$

Subtract $34$ from $4$ .

$3 x = - 30$

Divide each term in $3 x = - 30$ by $3$ and simplify.

Divide each term in $3 x = - 30$ by $3$ .

$\frac{3 x}{3} = \frac{- 30}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 30}{3}$

Divide $x$ by $1$ .

$x = \frac{- 30}{3}$

Simplify the right side.

Divide $- 30$ by $3$ .

$x = - 10$