Solve for w 3 = square root of 35-2w

$3 = \sqrt{35 - 2 w}$

Step 1

Rewrite the equation as $\sqrt{35 - 2 w} = 3$ .

$\sqrt{35 - 2 w} = 3$

Step 2

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

${\sqrt{35 - 2 w}}^{2} = 3^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{35 - 2 w}$ as ${(35 - 2 w)}^{\frac{1}{2}}$ .

${({(35 - 2 w)}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${({(35 - 2 w)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(35 - 2 w)}^{\frac{1}{2}})}^{2}$ .

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

${(35 - 2 w)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(35 - 2 w)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(35 - 2 w)}^{1} = 3^{2}$

Simplify.

$35 - 2 w = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$35 - 2 w = 9$

Step 4

Solve for $w$ .

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

Subtract $35$ from both sides of the equation.

$- 2 w = 9 - 35$

Subtract $35$ from $9$ .

$- 2 w = - 26$

Divide each term in $- 2 w = - 26$ by $- 2$ and simplify.

Divide each term in $- 2 w = - 26$ by $- 2$ .

$\frac{- 2 w}{- 2} = \frac{- 26}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 w}{- 2} = \frac{- 26}{- 2}$

Divide $w$ by $1$ .

$w = \frac{- 26}{- 2}$

Simplify the right side.

Divide $- 26$ by $- 2$ .

$w = 13$