Solve the Rational Equation for x square root of 3x-17+2=7

$\sqrt{3 x - 17} + 2 = 7$

Step 1

Move all terms not containing $\sqrt{3 x - 17}$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$\sqrt{3 x - 17} = 7 - 2$

Subtract $2$ from $7$ .

$\sqrt{3 x - 17} = 5$

Step 2

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

${\sqrt{3 x - 17}}^{2} = 5^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 17}$ as ${(3 x - 17)}^{\frac{1}{2}}$ .

${({(3 x - 17)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

Simplify ${({(3 x - 17)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x - 17)}^{\frac{1}{2}})}^{2}$ .

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

${(3 x - 17)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x - 17)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(3 x - 17)}^{1} = 5^{2}$

Simplify.

$3 x - 17 = 5^{2}$

Simplify the right side.

Raise $5$ to the power of $2$ .

$3 x - 17 = 25$

Step 4

Solve for $x$ .

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

Add $17$ to both sides of the equation.

$3 x = 25 + 17$

Add $25$ and $17$ .

$3 x = 42$

Divide each term in $3 x = 42$ by $3$ and simplify.

Divide each term in $3 x = 42$ by $3$ .

$\frac{3 x}{3} = \frac{42}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{42}{3}$

Divide $x$ by $1$ .

$x = \frac{42}{3}$

Simplify the right side.

Divide $42$ by $3$ .

$x = 14$

Solve the Rational Equation for x square root of 3x-17+2=7

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