Solve for s 2 = square root of 4s-4-4

$2 = \sqrt{4 s - 4} - 4$

Step 1

Rewrite the equation as $\sqrt{4 s - 4} - 4 = 2$ .

$\sqrt{4 s - 4} - 4 = 2$

Step 2

Move all terms not containing $\sqrt{4 s - 4}$ to the right side of the equation.

Add $4$ to both sides of the equation.

$\sqrt{4 s - 4} = 2 + 4$

Add $2$ and $4$ .

$\sqrt{4 s - 4} = 6$

Step 3

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

${\sqrt{4 s - 4}}^{2} = 6^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 s - 4}$ as ${(4 s - 4)}^{\frac{1}{2}}$ .

${({(4 s - 4)}^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

Simplify ${({(4 s - 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 s - 4)}^{\frac{1}{2}})}^{2}$ .

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

${(4 s - 4)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 s - 4)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

${(4 s - 4)}^{1} = 6^{2}$

Simplify.

$4 s - 4 = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$4 s - 4 = 36$

Step 5

Solve for $s$ .

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

Add $4$ to both sides of the equation.

$4 s = 36 + 4$

Add $36$ and $4$ .

$4 s = 40$

Divide each term in $4 s = 40$ by $4$ and simplify.

Divide each term in $4 s = 40$ by $4$ .

$\frac{4 s}{4} = \frac{40}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 s}{4} = \frac{40}{4}$

Divide $s$ by $1$ .

$s = \frac{40}{4}$

Simplify the right side.

Divide $40$ by $4$ .

$s = 10$

Solve for s 2 = square root of 4s-4-4

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