Finite Math Examples

$12 x^{2} = 147$

Step 1

Divide each term in $12 x^{2} = 147$ by $12$ and simplify.

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Step 1.1

Divide each term in $12 x^{2} = 147$ by $12$ .

$\frac{12 x^{2}}{12} = \frac{147}{12}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $12$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{12 x^{2}}{12} = \frac{147}{12}$

Step 1.2.1.2

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

$x^{2} = \frac{147}{12}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $147$ and $12$ .

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Step 1.3.1.1

Factor $3$ out of $147$ .

$x^{2} = \frac{3 (49)}{12}$

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $3$ out of $12$ .

$x^{2} = \frac{3 \cdot 49}{3 \cdot 4}$

Step 1.3.1.2.2

Cancel the common factor.

$x^{2} = \frac{3 \cdot 49}{3 \cdot 4}$

Step 1.3.1.2.3

Rewrite the expression.

$x^{2} = \frac{49}{4}$

Step 2

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

$x = \pm \sqrt{\frac{49}{4}}$

Step 3

Simplify $\pm \sqrt{\frac{49}{4}}$ .

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Step 3.1

Rewrite $\sqrt{\frac{49}{4}}$ as $\frac{\sqrt{49}}{\sqrt{4}}$ .

$x = \pm \frac{\sqrt{49}}{\sqrt{4}}$

Step 3.2

Simplify the numerator.

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Step 3.2.1

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

$x = \pm \frac{\sqrt{7^{2}}}{\sqrt{4}}$

Step 3.2.2

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

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

Step 3.3

Simplify the denominator.

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Step 3.3.1

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

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

Step 3.3.2

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

$x = \pm \frac{7}{2}$

Step 4

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

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Step 4.1

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

$x = \frac{7}{2}$

Step 4.2

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

$x = - \frac{7}{2}$

Step 4.3

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

$x = \frac{7}{2}, - \frac{7}{2}$