Algebra Examples

$c = \frac{1}{3} (a^{2} + b)$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (a^{2} + b) = c$ .

$\frac{1}{3} \cdot (a^{2} + b) = c$

Step 2

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (a^{2} + b)) = 3 c$

Step 3

Simplify the left side.

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Step 3.1

Simplify $3 (\frac{1}{3} \cdot (a^{2} + b))$ .

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Step 3.1.1

Apply the distributive property.

$3 (\frac{1}{3} a^{2} + \frac{1}{3} b) = 3 c$

Step 3.1.2

Combine $\frac{1}{3}$ and $a^{2}$ .

$3 (\frac{a^{2}}{3} + \frac{1}{3} b) = 3 c$

Step 3.1.3

Combine $\frac{1}{3}$ and $b$ .

$3 (\frac{a^{2}}{3} + \frac{b}{3}) = 3 c$

Step 3.1.4

Apply the distributive property.

$3 \frac{a^{2}}{3} + 3 \frac{b}{3} = 3 c$

Step 3.1.5

Cancel the common factor of $3$ .

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Step 3.1.5.1

Cancel the common factor.

$3 \frac{a^{2}}{3} + 3 \frac{b}{3} = 3 c$

Step 3.1.5.2

Rewrite the expression.

$a^{2} + 3 \frac{b}{3} = 3 c$

Step 3.1.6

Cancel the common factor of $3$ .

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Step 3.1.6.1

Cancel the common factor.

$a^{2} + 3 \frac{b}{3} = 3 c$

Step 3.1.6.2

Rewrite the expression.

$a^{2} + b = 3 c$

Step 4

Subtract $b$ from both sides of the equation.

$a^{2} = 3 c - b$

Step 5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$a = \pm \sqrt{3 c - b}$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

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Step 6.1

First, use the positive value of the $\pm$ to find the first solution.

$a = \sqrt{3 c - b}$

Step 6.2

Next, use the negative value of the $\pm$ to find the second solution.

$a = - \sqrt{3 c - b}$

Step 6.3

The complete solution is the result of both the positive and negative portions of the solution.

$a = \sqrt{3 c - b}$

$a = - \sqrt{3 c - b}$

$a = \sqrt{3 c - b}$

$a = - \sqrt{3 c - b}$