Finite Math Examples

$f (x) = 3 x^{2} - 6$

Step 1

Set $3 x^{2} - 6$ equal to $0$ .

$3 x^{2} - 6 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $6$ to both sides of the equation.

$3 x^{2} = 6$

Step 2.2

Divide each term in $3 x^{2} = 6$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x^{2} = 6$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{6}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{6}{3}$

Step 2.2.2.1.2

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

$x^{2} = \frac{6}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $6$ by $3$ .

$x^{2} = 2$

Step 2.3

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

$x = \pm \sqrt{2}$

Step 2.4

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

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Step 2.4.1

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

$x = \sqrt{2}$

Step 2.4.2

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

$x = - \sqrt{2}$

Step 2.4.3

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.41421356 \dots, - 1.41421356 \dots$

Step 4