Solve the Rational Equation for x 7+ square root of x=12

$7 + \sqrt{x} = 12$

Step 1

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

Subtract $7$ from both sides of the equation.

$\sqrt{x} = 12 - 7$

Subtract $7$ from $12$ .

$\sqrt{x} = 5$

Step 2

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

${\sqrt{x}}^{2} = 5^{2}$

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

$x^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

$x^{1} = 5^{2}$

Simplify.

$x = 5^{2}$

Simplify the right side.

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

$x = 25$