Solve the Rational Equation for x 5 square root of x+2=12

$5 \sqrt{x} + 2 = 12$

Move all terms not containing $5 \sqrt{x}$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$5 \sqrt{x} = 12 - 2$

Subtract $2$ from $12$ .

$5 \sqrt{x} = 10$

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

${(5 \sqrt{x})}^{2} = 10^{2}$

Simplify each side of the equation.

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

${(5 x^{\frac{1}{2}})}^{2} = 10^{2}$

Simplify the left side.

Simplify ${(5 x^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $5 x^{\frac{1}{2}}$ .

$5^{2} {(x^{\frac{1}{2}})}^{2} = 10^{2}$

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

$25 {(x^{\frac{1}{2}})}^{2} = 10^{2}$

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

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

$25 x^{\frac{1}{2} \cdot 2} = 10^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 x^{\frac{1}{2} \cdot 2} = 10^{2}$

Rewrite the expression.

$25 x^{1} = 10^{2}$

Simplify.

$25 x = 10^{2}$

Simplify the right side.

Raise $10$ to the power of $2$ .

$25 x = 100$

Divide each term in $25 x = 100$ by $25$ and simplify.

Divide each term in $25 x = 100$ by $25$ .

$\frac{25 x}{25} = \frac{100}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 x}{25} = \frac{100}{25}$

Divide $x$ by $1$ .

$x = \frac{100}{25}$

Simplify the right side.

Divide $100$ by $25$ .

$x = 4$