Calculus Examples

$\frac{28}{16} = t^{2}$

Step 1

Rewrite the equation as $t^{2} = \frac{28}{16}$ .

$t^{2} = \frac{28}{16}$

Step 2

Reduce the expression $\frac{28}{16}$ by cancelling the common factors.

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Step 2.1

Factor $4$ out of $28$ .

$t^{2} = \frac{4 (7)}{16}$

Step 2.2

Factor $4$ out of $16$ .

$t^{2} = \frac{4 \cdot 7}{4 \cdot 4}$

Step 2.3

Cancel the common factor.

$t^{2} = \frac{4 \cdot 7}{4 \cdot 4}$

Step 2.4

Rewrite the expression.

$t^{2} = \frac{7}{4}$

Step 3

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

$t = \pm \sqrt{\frac{7}{4}}$

Step 4

Simplify $\pm \sqrt{\frac{7}{4}}$ .

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Step 4.1

Rewrite $\sqrt{\frac{7}{4}}$ as $\frac{\sqrt{7}}{\sqrt{4}}$ .

$t = \pm \frac{\sqrt{7}}{\sqrt{4}}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Rewrite $4$ as $2^{2}$ .

$t = \pm \frac{\sqrt{7}}{\sqrt{2^{2}}}$

Step 4.2.2

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

$t = \pm \frac{\sqrt{7}}{2}$

Step 5

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

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Step 5.1

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

$t = \frac{\sqrt{7}}{2}$

Step 5.2

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

$t = - \frac{\sqrt{7}}{2}$

Step 5.3

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

$t = \frac{\sqrt{7}}{2}, - \frac{\sqrt{7}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = \frac{\sqrt{7}}{2}, - \frac{\sqrt{7}}{2}$

Decimal Form:

$t = 1.32287565 \dots, - 1.32287565 \dots$