Pre-Algebra Examples

$81 - \frac{1}{25} x^{2} = 0$

Step 1

Combine $x^{2}$ and $\frac{1}{25}$ .

$81 - \frac{x^{2}}{25} = 0$

Step 2

Subtract $81$ from both sides of the equation.

$- \frac{x^{2}}{25} = - 81$

Step 3

Multiply both sides of the equation by $- 25$ .

$- 25 (- \frac{x^{2}}{25}) = - 25 \cdot - 81$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- 25 (- \frac{x^{2}}{25})$ .

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Step 4.1.1.1

Cancel the common factor of $25$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{x^{2}}{25}$ into the numerator.

$- 25 \frac{- x^{2}}{25} = - 25 \cdot - 81$

Step 4.1.1.1.2

Factor $25$ out of $- 25$ .

$25 (- 1) \frac{- x^{2}}{25} = - 25 \cdot - 81$

Step 4.1.1.1.3

Cancel the common factor.

$25 \cdot - 1 \frac{- x^{2}}{25} = - 25 \cdot - 81$

Step 4.1.1.1.4

Rewrite the expression.

$- - x^{2} = - 25 \cdot - 81$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x^{2} = - 25 \cdot - 81$

Step 4.1.1.2.2

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

$x^{2} = - 25 \cdot - 81$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 25$ by $- 81$ .

$x^{2} = 2025$

Step 5

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

$x = \pm \sqrt{2025}$

Step 6

Simplify $\pm \sqrt{2025}$ .

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Step 6.1

Rewrite $2025$ as $45^{2}$ .

$x = \pm \sqrt{45^{2}}$

Step 6.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 45$

Step 7

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

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Step 7.1

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

$x = 45$

Step 7.2

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

$x = - 45$

Step 7.3

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

$x = 45, - 45$