Solve for w 15=6+ square root of 3w-9

$15 = 6 + \sqrt{3 w - 9}$

Step 1

Rewrite the equation as $6 + \sqrt{3 w - 9} = 15$ .

$6 + \sqrt{3 w - 9} = 15$

Step 2

Move all terms not containing $\sqrt{3 w - 9}$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$\sqrt{3 w - 9} = 15 - 6$

Subtract $6$ from $15$ .

$\sqrt{3 w - 9} = 9$

Step 3

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

${\sqrt{3 w - 9}}^{2} = 9^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 w - 9}$ as ${(3 w - 9)}^{\frac{1}{2}}$ .

${({(3 w - 9)}^{\frac{1}{2}})}^{2} = 9^{2}$

Simplify the left side.

Simplify ${({(3 w - 9)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 w - 9)}^{\frac{1}{2}})}^{2}$ .

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

${(3 w - 9)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 w - 9)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Rewrite the expression.

${(3 w - 9)}^{1} = 9^{2}$

Simplify.

$3 w - 9 = 9^{2}$

Simplify the right side.

Raise $9$ to the power of $2$ .

$3 w - 9 = 81$

Step 5

Solve for $w$ .

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

Add $9$ to both sides of the equation.

$3 w = 81 + 9$

Add $81$ and $9$ .

$3 w = 90$

Divide each term in $3 w = 90$ by $3$ and simplify.

Divide each term in $3 w = 90$ by $3$ .

$\frac{3 w}{3} = \frac{90}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 w}{3} = \frac{90}{3}$

Divide $w$ by $1$ .

$w = \frac{90}{3}$

Simplify the right side.

Divide $90$ by $3$ .

$w = 30$

Solve for w 15=6+ square root of 3w-9

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