Finite Math Examples

$m^{2} - 5 m - 5$

Step 1

Set $m^{2} - 5 m - 5$ equal to $0$ .

$m^{2} - 5 m - 5 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 1$ , $b = - 5$ , and $c = - 5$ into the quadratic formula and solve for $m$ .

$\frac{5 \pm \sqrt{{(- 5)}^{2} - 4 \cdot (1 \cdot - 5)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 5$ to the power of $2$ .

$m = \frac{5 \pm \sqrt{25 - 4 \cdot 1 \cdot - 5}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 5$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$m = \frac{5 \pm \sqrt{25 - 4 \cdot - 5}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 5$ .

$m = \frac{5 \pm \sqrt{25 + 20}}{2 \cdot 1}$

Step 4.1.3

Add $25$ and $20$ .

$m = \frac{5 \pm \sqrt{45}}{2 \cdot 1}$

Step 4.1.4

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 4.1.4.1

Factor $9$ out of $45$ .

$m = \frac{5 \pm \sqrt{9 (5)}}{2 \cdot 1}$

Step 4.1.4.2

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

$m = \frac{5 \pm \sqrt{3^{2} \cdot 5}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical.

$m = \frac{5 \pm 3 \sqrt{5}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$m = \frac{5 \pm 3 \sqrt{5}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$m = \frac{5 \pm 3 \sqrt{5}}{2}$

Decimal Form:

$m = 5.85410196 \dots, - 0.85410196 \dots$