Finite Math Examples

$f (x) = 3 x^{2} + 5 - 2$

Step 1

Set $3 x^{2} + 5 - 2$ equal to $0$ .

$3 x^{2} + 5 - 2 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $2$ from $5$ .

$3 x^{2} + 3 = 0$

Step 2.2

Subtract $3$ from both sides of the equation.

$3 x^{2} = - 3$

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $3$ .

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Step 2.3.2.1.1

Cancel the common factor.

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

Step 2.3.2.1.2

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

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 3$ by $3$ .

$x^{2} = - 1$

Step 2.4

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

$x = \pm \sqrt{- 1}$

Step 2.5

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i$

Step 2.6

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

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Step 2.6.1

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

$x = i$

Step 2.6.2

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

$x = - i$

Step 2.6.3

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

$x = i, - i$

Step 3