Pre-Algebra Examples

$\frac{23 - x^{2}}{8} = 0$

Step 1

Set the numerator equal to zero.

$23 - x^{2} = 0$

Step 2

Solve the equation for $x$ .

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Step 2.1

Subtract $23$ from both sides of the equation.

$- x^{2} = - 23$

Step 2.2

Divide each term in $- x^{2} = - 23$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- x^{2} = - 23$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 23}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 23}{- 1}$

Step 2.2.2.2

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

$x^{2} = \frac{- 23}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 23$ by $- 1$ .

$x^{2} = 23$

Step 2.3

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

$x = \pm \sqrt{23}$

Step 2.4

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

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Step 2.4.1

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

$x = \sqrt{23}$

Step 2.4.2

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

$x = - \sqrt{23}$

Step 2.4.3

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

$x = \sqrt{23}, - \sqrt{23}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{23}, - \sqrt{23}$

Decimal Form:

$x = 4.79583152 \dots, - 4.79583152 \dots$