Algebra Examples

$0 = 15 - 3 x^{2}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $15$ from both sides of the equation.

$- 15 = - 3 x^{2}$

Step 1.2

Add $3 x^{2}$ to both sides of the equation.

$- 15 + 3 x^{2} = 0$

Step 2

Factor $3$ out of $- 15 + 3 x^{2}$ .

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Step 2.1

Factor $3$ out of $- 15$ .

$3 \cdot - 5 + 3 x^{2} = 0$

Step 2.2

Factor $3$ out of $3 \cdot - 5 + 3 x^{2}$ .

$3 (- 5 + x^{2}) = 0$

Step 3

Divide each term in $3 (- 5 + x^{2}) = 0$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 (- 5 + x^{2}) = 0$ by $3$ .

$\frac{3 (- 5 + x^{2})}{3} = \frac{0}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 (- 5 + x^{2})}{3} = \frac{0}{3}$

Step 3.2.1.2

Divide $- 5 + x^{2}$ by $1$ .

$- 5 + x^{2} = \frac{0}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $3$ .

$- 5 + x^{2} = 0$

Step 4

Add $5$ to both sides of the equation.

$x^{2} = 5$

Step 5

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

$x = \pm \sqrt{5}$

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.

$x = \sqrt{5}$

Step 6.2

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

$x = - \sqrt{5}$

Step 6.3

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 2.23606797 \dots, - 2.23606797 \dots$