Algebra Examples

$\sqrt{6 q - 5} = 5$

Step 1

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

${\sqrt{6 q - 5}}^{2} = 5^{2}$

Step 2

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$6 q - 5 = 5^{2}$

Simplify the right side.

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Raise $5$ to the power of $2$ .

$6 q - 5 = 25$

Step 3

Solve for $q$ .

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

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Add $5$ to both sides of the equation.

$6 q = 25 + 5$

Add $25$ and $5$ .

$6 q = 30$

Divide each term in $6 q = 30$ by $6$ and simplify.

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Divide each term in $6 q = 30$ by $6$ .

$\frac{6 q}{6} = \frac{30}{6}$

Simplify the left side.

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Cancel the common factor of $6$ .

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Cancel the common factor.

$\frac{6 q}{6} = \frac{30}{6}$

Divide $q$ by $1$ .

$q = \frac{30}{6}$

Simplify the right side.

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Divide $30$ by $6$ .

$q = 5$