Solve by Factoring 5 square root of x+2=12

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

Step 1

Subtract $12$ from both sides of the equation.

$5 \sqrt{x} + 2 - 12 = 0$

Step 2

Subtract $12$ from $2$ .

$5 \sqrt{x} - 10 = 0$

Step 3

Factor $5$ out of $5 \sqrt{x} - 10$ .

Factor $5$ out of $5 \sqrt{x}$ .

$5 (\sqrt{x}) - 10 = 0$

Factor $5$ out of $- 10$ .

$5 \sqrt{x} + 5 \cdot - 2 = 0$

Factor $5$ out of $5 \sqrt{x} + 5 \cdot - 2$ .

$5 (\sqrt{x} - 2) = 0$

Step 4

Divide each term in $5 (\sqrt{x} - 2) = 0$ by $5$ and simplify.

Divide each term in $5 (\sqrt{x} - 2) = 0$ by $5$ .

$\frac{5 (\sqrt{x} - 2)}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 (\sqrt{x} - 2)}{5} = \frac{0}{5}$

Divide $\sqrt{x} - 2$ by $1$ .

$\sqrt{x} - 2 = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$\sqrt{x} - 2 = 0$

Step 5

Add $2$ to both sides of the equation.

$\sqrt{x} = 2$

Step 6

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

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

Step 7

Simplify each side of the equation.

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

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

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, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x = 2^{2}$

Simplify the right side.

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

$x = 4$

Solve by Factoring 5 square root of x+2=12

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