Finite Math Examples

$\frac{49}{2} = (2) \cdot (16 x^{2})$

Step 1

Rewrite the equation as $2 \cdot (16 x^{2}) = \frac{49}{2}$ .

$2 \cdot (16 x^{2}) = \frac{49}{2}$

Step 2

Multiply $16$ by $2$ .

$32 \cdot x^{2} = \frac{49}{2}$

Step 3

Divide each term in $32 \cdot x^{2} = \frac{49}{2}$ by $32$ and simplify.

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Step 3.1

Divide each term in $32 \cdot x^{2} = \frac{49}{2}$ by $32$ .

$\frac{32 \cdot x^{2}}{32} = \frac{\frac{49}{2}}{32}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $32$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{32 \cdot x^{2}}{32} = \frac{\frac{49}{2}}{32}$

Step 3.2.1.2

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

$x^{2} = \frac{\frac{49}{2}}{32}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x^{2} = \frac{49}{2} \cdot \frac{1}{32}$

Step 3.3.2

Multiply $\frac{49}{2} \cdot \frac{1}{32}$ .

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Step 3.3.2.1

Multiply $\frac{49}{2}$ by $\frac{1}{32}$ .

$x^{2} = \frac{49}{2 \cdot 32}$

Step 3.3.2.2

Multiply $2$ by $32$ .

$x^{2} = \frac{49}{64}$

Step 4

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

$x = \pm \sqrt{\frac{49}{64}}$

Step 5

Simplify $\pm \sqrt{\frac{49}{64}}$ .

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Step 5.1

Rewrite $\sqrt{\frac{49}{64}}$ as $\frac{\sqrt{49}}{\sqrt{64}}$ .

$x = \pm \frac{\sqrt{49}}{\sqrt{64}}$

Step 5.2

Simplify the numerator.

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Step 5.2.1

Rewrite $49$ as $7^{2}$ .

$x = \pm \frac{\sqrt{7^{2}}}{\sqrt{64}}$

Step 5.2.2

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

$x = \pm \frac{7}{\sqrt{64}}$

Step 5.3

Simplify the denominator.

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Step 5.3.1

Rewrite $64$ as $8^{2}$ .

$x = \pm \frac{7}{\sqrt{8^{2}}}$

Step 5.3.2

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

$x = \pm \frac{7}{8}$

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.

$x = \frac{7}{8}$

Step 6.2

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

$x = - \frac{7}{8}$

Step 6.3

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

$x = \frac{7}{8}, - \frac{7}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{8}, - \frac{7}{8}$

Decimal Form:

$x = 0.875, - 0.875$