Solve by Factoring square root of q-9=7

$\sqrt{q - 9} = 7$

Step 1

Subtract $7$ from both sides of the equation.

$\sqrt{q - 9} - 7 = 0$

Step 2

Add $7$ to both sides of the equation.

$\sqrt{q - 9} = 7$

Step 3

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

${\sqrt{q - 9}}^{2} = 7^{2}$

Step 4

Simplify each side of the equation.

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

${({(q - 9)}^{\frac{1}{2}})}^{2} = 7^{2}$

Simplify the left side.

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

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

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

${(q - 9)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(q - 9)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Rewrite the expression.

${(q - 9)}^{1} = 7^{2}$

Simplify.

$q - 9 = 7^{2}$

Simplify the right side.

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

$q - 9 = 49$

Step 5

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

Add $9$ to both sides of the equation.

$q = 49 + 9$

Add $49$ and $9$ .

$q = 58$