Finite Math Examples

$(x^{2} + 10 x) + 12$

Step 1

Set $(x^{2} + 10 x) + 12$ equal to $0$ .

$(x^{2} + 10 x) + 12 = 0$

Step 2

Simplify the left side.

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Step 2.1

Remove parentheses.

$x^{2} + 10 x + 12 = 0$

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 $a = 1$ , $b = 10$ , and $c = 12$ into the quadratic formula and solve for $x$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (1 \cdot 12)}}{2 \cdot 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $10$ to the power of $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 1 \cdot 12}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4 \cdot 1 \cdot 12$ .

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Step 5.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 12}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $12$ .

$x = \frac{- 10 \pm \sqrt{100 - 48}}{2 \cdot 1}$

Step 5.1.3

Subtract $48$ from $100$ .

$x = \frac{- 10 \pm \sqrt{52}}{2 \cdot 1}$

Step 5.1.4

Rewrite $52$ as $2^{2} \cdot 13$ .

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Step 5.1.4.1

Factor $4$ out of $52$ .

$x = \frac{- 10 \pm \sqrt{4 (13)}}{2 \cdot 1}$

Step 5.1.4.2

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

$x = \frac{- 10 \pm \sqrt{2^{2} \cdot 13}}{2 \cdot 1}$

Step 5.1.5

Pull terms out from under the radical.

$x = \frac{- 10 \pm 2 \sqrt{13}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$x = \frac{- 10 \pm 2 \sqrt{13}}{2}$

Step 5.3

Simplify $\frac{- 10 \pm 2 \sqrt{13}}{2}$ .

$x = - 5 \pm \sqrt{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - 5 \pm \sqrt{13}$

Decimal Form:

$x = - 1.39444872 \dots, - 8.60555127 \dots$