Solve for w square root of w^2-20-2=2

$\sqrt{w^{2} - 20} - 2 = 2$

Step 1

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

${(w^{2} - 20)}^{\frac{1}{2}} - 2 = 2$

Step 2

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

Add $2$ to both sides of the equation.

${(w^{2} - 20)}^{\frac{1}{2}} = 2 + 2$

Add $2$ and $2$ .

${(w^{2} - 20)}^{\frac{1}{2}} = 4$

Step 3

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${({(w^{2} - 20)}^{\frac{1}{2}})}^{2} = 4^{2}$

Step 4

Simplify the exponent.

Simplify the left side.

Simplify ${({(w^{2} - 20)}^{\frac{1}{2}})}^{2}$ .

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

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

${(w^{2} - 20)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(w^{2} - 20)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(w^{2} - 20)}^{1} = 4^{2}$

Simplify.

$w^{2} - 20 = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$w^{2} - 20 = 16$

Step 5

Solve for $w$ .

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

Add $20$ to both sides of the equation.

$w^{2} = 16 + 20$

Add $16$ and $20$ .

$w^{2} = 36$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$w = \pm \sqrt{36}$

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$w = \pm \sqrt{6^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$w = \pm 6$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$w = 6$

Next, use the negative value of the $\pm$ to find the second solution.

$w = - 6$

The complete solution is the result of both the positive and negative portions of the solution.

$w = 6, - 6$

Solve for w square root of w^2-20-2=2

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