Solve for w square root of 6w-5+10=3

$\sqrt{6 w - 5} + 10 = 3$

Step 1

Move all terms not containing $\sqrt{6 w - 5}$ to the right side of the equation.

Subtract $10$ from both sides of the equation.

$\sqrt{6 w - 5} = 3 - 10$

Subtract $10$ from $3$ .

$\sqrt{6 w - 5} = - 7$

Step 2

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

${\sqrt{6 w - 5}}^{2} = {(- 7)}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 w - 5}$ as ${(6 w - 5)}^{\frac{1}{2}}$ .

${({(6 w - 5)}^{\frac{1}{2}})}^{2} = {(- 7)}^{2}$

Simplify the left side.

Simplify ${({(6 w - 5)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(6 w - 5)}^{\frac{1}{2}})}^{2}$ .

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

${(6 w - 5)}^{\frac{1}{2} \cdot 2} = {(- 7)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(6 w - 5)}^{\frac{1}{2} \cdot 2} = {(- 7)}^{2}$

Rewrite the expression.

${(6 w - 5)}^{1} = {(- 7)}^{2}$

Simplify.

$6 w - 5 = {(- 7)}^{2}$

Simplify the right side.

Raise $- 7$ to the power of $2$ .

$6 w - 5 = 49$

Step 4

Solve for $w$ .

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

Add $5$ to both sides of the equation.

$6 w = 49 + 5$

Add $49$ and $5$ .

$6 w = 54$

Divide each term in $6 w = 54$ by $6$ and simplify.

Divide each term in $6 w = 54$ by $6$ .

$\frac{6 w}{6} = \frac{54}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 w}{6} = \frac{54}{6}$

Divide $w$ by $1$ .

$w = \frac{54}{6}$

Simplify the right side.

Divide $54$ by $6$ .

$w = 9$

Step 5

Exclude the solutions that do not make $\sqrt{6 w - 5} + 10 = 3$ true.

$No solution$

Solve for w square root of 6w-5+10=3

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