Finite Math Examples

$m (m - 5) - 3 = 0$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$m \cdot m + m \cdot - 5 - 3 = 0$

Step 1.2

Multiply $m$ by $m$ .

$m^{2} + m \cdot - 5 - 3 = 0$

Step 1.3

Move $- 5$ to the left of $m$ .

$m^{2} - 5 m - 3 = 0$

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 $c = - 3$ into the quadratic formula and solve for $m$ .

$\frac{5 \pm \sqrt{{(- 5)}^{2} - 4 \cdot (1 \cdot - 3)}}{2 \cdot 1}$

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 $2$ .

$m = \frac{5 \pm \sqrt{25 - 4 \cdot 1 \cdot - 3}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 3$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$m = \frac{5 \pm \sqrt{25 - 4 \cdot - 3}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 3$ .

$m = \frac{5 \pm \sqrt{25 + 12}}{2 \cdot 1}$

Step 4.1.3

Add $25$ and $12$ .

$m = \frac{5 \pm \sqrt{37}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$m = \frac{5 \pm \sqrt{37}}{2}$

Step 5

The final answer is the combination of both solutions.

$m = \frac{5 + \sqrt{37}}{2}, \frac{5 - \sqrt{37}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = \frac{5 + \sqrt{37}}{2}, \frac{5 - \sqrt{37}}{2}$

Decimal Form:

$m = 5.54138126 \dots, - 0.54138126 \dots$