Basic Math Examples

$2 c^{2} + 54 = 0$

Step 1

Subtract $54$ from both sides of the equation.

$2 c^{2} = - 54$

Step 2

Divide each term in $2 c^{2} = - 54$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 c^{2} = - 54$ by $2$ .

$\frac{2 c^{2}}{2} = \frac{- 54}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 c^{2}}{2} = \frac{- 54}{2}$

Step 2.2.1.2

Divide $c^{2}$ by $1$ .

$c^{2} = \frac{- 54}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 54$ by $2$ .

$c^{2} = - 27$

Step 3

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

$c = \pm \sqrt{- 27}$

Step 4

Simplify $\pm \sqrt{- 27}$ .

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Step 4.1

Rewrite $- 27$ as $- 1 (27)$ .

$c = \pm \sqrt{- 1 (27)}$

Step 4.2

Rewrite $\sqrt{- 1 (27)}$ as $\sqrt{- 1} \cdot \sqrt{27}$ .

$c = \pm \sqrt{- 1} \cdot \sqrt{27}$

Step 4.3

Rewrite $\sqrt{- 1}$ as $i$ .

$c = \pm i \cdot \sqrt{27}$

Step 4.4

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 4.4.1

Factor $9$ out of $27$ .

$c = \pm i \cdot \sqrt{9 (3)}$

Step 4.4.2

Rewrite $9$ as $3^{2}$ .

$c = \pm i \cdot \sqrt{3^{2} \cdot 3}$

Step 4.5

Pull terms out from under the radical.

$c = \pm i \cdot (3 \sqrt{3})$

Step 4.6

Move $3$ to the left of $i$ .

$c = \pm 3 i \sqrt{3}$

Step 5

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

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Step 5.1

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

$c = 3 i \sqrt{3}$

Step 5.2

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

$c = - 3 i \sqrt{3}$

Step 5.3

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

$c = 3 i \sqrt{3}, - 3 i \sqrt{3}$