Solve for x 1/2 square root of 20+x=5

$\frac{1}{2} \sqrt{20 + x} = 5$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot \sqrt{20 + x}) = 2 \cdot 5$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot \sqrt{20 + x})$ .

Combine $\frac{1}{2}$ and $\sqrt{20 + x}$ .

$2 \frac{\sqrt{20 + x}}{2} = 2 \cdot 5$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{\sqrt{20 + x}}{2} = 2 \cdot 5$

Rewrite the expression.

$\sqrt{20 + x} = 2 \cdot 5$

Simplify the right side.

Multiply $2$ by $5$ .

$\sqrt{20 + x} = 10$

Step 3

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

${\sqrt{20 + x}}^{2} = 10^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{20 + x}$ as ${(20 + x)}^{\frac{1}{2}}$ .

${({(20 + x)}^{\frac{1}{2}})}^{2} = 10^{2}$

Simplify the left side.

Simplify ${({(20 + x)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(20 + x)}^{\frac{1}{2}})}^{2}$ .

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

${(20 + x)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(20 + x)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Rewrite the expression.

${(20 + x)}^{1} = 10^{2}$

Simplify.

$20 + x = 10^{2}$

Simplify the right side.

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

$20 + x = 100$

Step 5

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

Subtract $20$ from both sides of the equation.

$x = 100 - 20$

Subtract $20$ from $100$ .

$x = 80$

Solve for x 1/2 square root of 20+x=5

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