Algebra Examples

$0.75 d = \frac{s^{2}}{30.25}$

Step 1

Rewrite the equation as $\frac{s^{2}}{30.25} = 0.75 d$ .

$\frac{s^{2}}{30.25} = 0.75 d$

Step 2

Multiply both sides of the equation by $30.25$ .

$30.25 \frac{s^{2}}{30.25} = 30.25 (0.75 d)$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $30.25$ .

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Step 3.1.1.1

Cancel the common factor.

$30.25 \frac{s^{2}}{30.25} = 30.25 (0.75 d)$

Step 3.1.1.2

Rewrite the expression.

$s^{2} = 30.25 (0.75 d)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $0.75$ by $30.25$ .

$s^{2} = 22.6875 d$

Step 4

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

$s = \pm \sqrt{22.6875 d}$

Step 5

Simplify $\pm \sqrt{22.6875 d}$ .

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Step 5.1

Rewrite $22.6875 d$ as ${({2.18246184}^{2})}^{2} d$ .

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Step 5.1.1

Rewrite $22.6875$ as ${4.76313972}^{2}$ .

$s = \pm \sqrt{{4.76313972}^{2} d}$

Step 5.1.2

Rewrite $4.76313972$ as ${2.18246184}^{2}$ .

$s = \pm \sqrt{{({2.18246184}^{2})}^{2} d}$

Step 5.2

Pull terms out from under the radical.

$s = \pm {2.18246184}^{2} \sqrt{d}$

Step 5.3

Raise $2.18246184$ to the power of $2$ .

$s = \pm 4.76313972 \sqrt{d}$

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.

$s = 4.76313972 \sqrt{d}$

Step 6.2

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

$s = - 4.76313972 \sqrt{d}$

Step 6.3

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

$s = 4.76313972 \sqrt{d}$

$s = - 4.76313972 \sqrt{d}$

$s = 4.76313972 \sqrt{d}$

$s = - 4.76313972 \sqrt{d}$