Finite Math Examples

$C (x) = 9 x^{2} - 8$

Step 1

Set $9 x^{2} - 8$ equal to $0$ .

$9 x^{2} - 8 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $8$ to both sides of the equation.

$9 x^{2} = 8$

Step 2.2

Divide each term in $9 x^{2} = 8$ by $9$ and simplify.

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Step 2.2.1

Divide each term in $9 x^{2} = 8$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{8}{9}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $9$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{8}{9}$

Step 2.2.2.1.2

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

$x^{2} = \frac{8}{9}$

Step 2.3

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

$x = \pm \sqrt{\frac{8}{9}}$

Step 2.4

Simplify $\pm \sqrt{\frac{8}{9}}$ .

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Step 2.4.1

Rewrite $\sqrt{\frac{8}{9}}$ as $\frac{\sqrt{8}}{\sqrt{9}}$ .

$x = \pm \frac{\sqrt{8}}{\sqrt{9}}$

Step 2.4.2

Simplify the numerator.

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Step 2.4.2.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 2.4.2.1.1

Factor $4$ out of $8$ .

$x = \pm \frac{\sqrt{4 (2)}}{\sqrt{9}}$

Step 2.4.2.1.2

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

$x = \pm \frac{\sqrt{2^{2} \cdot 2}}{\sqrt{9}}$

Step 2.4.2.2

Pull terms out from under the radical.

$x = \pm \frac{2 \sqrt{2}}{\sqrt{9}}$

Step 2.4.3

Simplify the denominator.

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Step 2.4.3.1

Rewrite $9$ as $3^{2}$ .

$x = \pm \frac{2 \sqrt{2}}{\sqrt{3^{2}}}$

Step 2.4.3.2

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

$x = \pm \frac{2 \sqrt{2}}{3}$

Step 2.5

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

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Step 2.5.1

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

$x = \frac{2 \sqrt{2}}{3}$

Step 2.5.2

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

$x = - \frac{2 \sqrt{2}}{3}$

Step 2.5.3

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

$x = \frac{2 \sqrt{2}}{3}, - \frac{2 \sqrt{2}}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2 \sqrt{2}}{3}, - \frac{2 \sqrt{2}}{3}$

Decimal Form:

$x = 0.94280904 \dots, - 0.94280904 \dots$

Step 4