Algebra Examples

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

Step 1

Subtract $3$ from both sides of the equation.

$- x^{2} = - 3$

Step 2

Divide each term in $- x^{2} = - 3$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- x^{2} = - 3$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 3}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 3}{- 1}$

Step 2.2.2

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

$x^{2} = \frac{- 3}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 3$ by $- 1$ .

$x^{2} = 3$

Step 3

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

$x = \pm \sqrt{3}$

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.

$x = \sqrt{3}$

Step 4.2

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

$x = - \sqrt{3}$

Step 4.3

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

$x = \sqrt{3}, - \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{3}, - \sqrt{3}$

Decimal Form:

$x = 1.73205080 \dots, - 1.73205080 \dots$

Step 6