Solve for q square root of 10q-9=9

$\sqrt{10 q - 9} = 9$

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

${\sqrt{10 q - 9}}^{2} = 9^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10 q - 9}$ as ${(10 q - 9)}^{\frac{1}{2}}$ .

${({(10 q - 9)}^{\frac{1}{2}})}^{2} = 9^{2}$

Simplify the left side.

Simplify ${({(10 q - 9)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(10 q - 9)}^{\frac{1}{2}})}^{2}$ .

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

${(10 q - 9)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(10 q - 9)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Rewrite the expression.

${(10 q - 9)}^{1} = 9^{2}$

Simplify.

$10 q - 9 = 9^{2}$

Simplify the right side.

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

$10 q - 9 = 81$

Solve for $q$ .

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

Add $9$ to both sides of the equation.

$10 q = 81 + 9$

Add $81$ and $9$ .

$10 q = 90$

Divide each term in $10 q = 90$ by $10$ and simplify.

Divide each term in $10 q = 90$ by $10$ .

$\frac{10 q}{10} = \frac{90}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 q}{10} = \frac{90}{10}$

Divide $q$ by $1$ .

$q = \frac{90}{10}$

Simplify the right side.

Divide $90$ by $10$ .

$q = 9$