Solve the Rational Equation for x 17-2 square root of 3x+10=1

$17 - 2 \sqrt{3 x + 10} = 1$

Move all terms not containing $- 2 \sqrt{3 x + 10}$ to the right side of the equation.

Subtract $17$ from both sides of the equation.

$- 2 \sqrt{3 x + 10} = 1 - 17$

Subtract $17$ from $1$ .

$- 2 \sqrt{3 x + 10} = - 16$

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

${(- 2 \sqrt{3 x + 10})}^{2} = {(- 16)}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x + 10}$ as ${(3 x + 10)}^{\frac{1}{2}}$ .

${(- 2 {(3 x + 10)}^{\frac{1}{2}})}^{2} = {(- 16)}^{2}$

Simplify the left side.

Simplify ${(- 2 {(3 x + 10)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 2 {(3 x + 10)}^{\frac{1}{2}}$ .

${(- 2)}^{2} {({(3 x + 10)}^{\frac{1}{2}})}^{2} = {(- 16)}^{2}$

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

$4 {({(3 x + 10)}^{\frac{1}{2}})}^{2} = {(- 16)}^{2}$

Multiply the exponents in ${({(3 x + 10)}^{\frac{1}{2}})}^{2}$ .

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

$4 {(3 x + 10)}^{\frac{1}{2} \cdot 2} = {(- 16)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(3 x + 10)}^{\frac{1}{2} \cdot 2} = {(- 16)}^{2}$

Rewrite the expression.

$4 {(3 x + 10)}^{1} = {(- 16)}^{2}$

Simplify.

$4 (3 x + 10) = {(- 16)}^{2}$

Apply the distributive property.

$4 (3 x) + 4 \cdot 10 = {(- 16)}^{2}$

Multiply.

Multiply $3$ by $4$ .

$12 x + 4 \cdot 10 = {(- 16)}^{2}$

Multiply $4$ by $10$ .

$12 x + 40 = {(- 16)}^{2}$

Simplify the right side.

Raise $- 16$ to the power of $2$ .

$12 x + 40 = 256$

Solve for $x$ .

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

Subtract $40$ from both sides of the equation.

$12 x = 256 - 40$

Subtract $40$ from $256$ .

$12 x = 216$

Divide each term in $12 x = 216$ by $12$ and simplify.

Divide each term in $12 x = 216$ by $12$ .

$\frac{12 x}{12} = \frac{216}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{216}{12}$

Divide $x$ by $1$ .

$x = \frac{216}{12}$

Simplify the right side.

Divide $216$ by $12$ .

$x = 18$

Solve the Rational Equation for x 17-2 square root of 3x+10=1

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