Finite Math Examples

$(x + x^{2} - 2) (- 3)$

Step 1

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

$(x + x^{2} - 2) (- 3) = 0$

Step 2

Simplify the left side.

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Step 2.1

Simplify $(x + x^{2} - 2) (- 3)$ .

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Step 2.1.1

Apply the distributive property.

$x \cdot - 3 + x^{2} \cdot - 3 - 2 \cdot - 3 = 0$

Step 2.1.2

Simplify.

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Step 2.1.2.1

Move $- 3$ to the left of $x$ .

$- 3 \cdot x + x^{2} \cdot - 3 - 2 \cdot - 3 = 0$

Step 2.1.2.2

Move $- 3$ to the left of $x^{2}$ .

$- 3 \cdot x - 3 \cdot x^{2} - 2 \cdot - 3 = 0$

Step 2.1.2.3

Multiply $- 2$ by $- 3$ .

$- 3 \cdot x - 3 \cdot x^{2} + 6 = 0$

Step 2.1.3

Multiply $- 3$ by $x^{2}$ .

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

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = - 3$ , $b = - 3$ , and $c = 6$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (- 3 \cdot 6)}}{2 \cdot - 3}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot - 3 \cdot 6}}{2 \cdot - 3}$

Step 5.1.2

Multiply $- 4 \cdot - 3 \cdot 6$ .

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Step 5.1.2.1

Multiply $- 4$ by $- 3$ .

$x = \frac{3 \pm \sqrt{9 + 12 \cdot 6}}{2 \cdot - 3}$

Step 5.1.2.2

Multiply $12$ by $6$ .

$x = \frac{3 \pm \sqrt{9 + 72}}{2 \cdot - 3}$

Step 5.1.3

Add $9$ and $72$ .

$x = \frac{3 \pm \sqrt{81}}{2 \cdot - 3}$

Step 5.1.4

Rewrite $81$ as $9^{2}$ .

$x = \frac{3 \pm \sqrt{9^{2}}}{2 \cdot - 3}$

Step 5.1.5

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

$x = \frac{3 \pm 9}{2 \cdot - 3}$

Step 5.2

Multiply $2$ by $- 3$ .

$x = \frac{3 \pm 9}{- 6}$

Step 5.3

Simplify $\frac{3 \pm 9}{- 6}$ .

$x = \frac{1 \pm 3}{- 2}$

Step 5.4

Move the negative in front of the fraction.

$x = - \frac{1 \pm 3}{2}$

Step 6

The final answer is the combination of both solutions.

$x = - 2, 1$