Algebra Examples

$- 3 x^{2} = 150$

Step 1

Divide each term in $- 3 x^{2} = 150$ by $- 3$ and simplify.

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Step 1.1

Divide each term in $- 3 x^{2} = 150$ by $- 3$ .

$\frac{- 3 x^{2}}{- 3} = \frac{150}{- 3}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{- 3 x^{2}}{- 3} = \frac{150}{- 3}$

Step 1.2.1.2

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

$x^{2} = \frac{150}{- 3}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $150$ by $- 3$ .

$x^{2} = - 50$

Step 2

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

$x = \pm \sqrt{- 50}$

Step 3

Simplify $\pm \sqrt{- 50}$ .

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Step 3.1

Rewrite $- 50$ as $- 1 (50)$ .

$x = \pm \sqrt{- 1 (50)}$

Step 3.2

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{50}$

Step 3.3

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

$x = \pm i \cdot \sqrt{50}$

Step 3.4

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 3.4.1

Factor $25$ out of $50$ .

$x = \pm i \cdot \sqrt{25 (2)}$

Step 3.4.2

Rewrite $25$ as $5^{2}$ .

$x = \pm i \cdot \sqrt{5^{2} \cdot 2}$

Step 3.5

Pull terms out from under the radical.

$x = \pm i \cdot (5 \sqrt{2})$

Step 3.6

Move $5$ to the left of $i$ .

$x = \pm 5 i \sqrt{2}$

Step 4

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

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Step 4.1

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

$x = 5 i \sqrt{2}$

Step 4.2

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

$x = - 5 i \sqrt{2}$

Step 4.3

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

$x = 5 i \sqrt{2}, - 5 i \sqrt{2}$