Precalculus Examples

$5 m^{2} - 7 m = 5$

Step 1

Subtract $5$ from both sides of the equation.

$5 m^{2} - 7 m - 5 = 0$

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 $a = 5$ , $b = - 7$ , and $c = - 5$ into the quadratic formula and solve for $m$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (5 \cdot - 5)}}{2 \cdot 5}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 7$ to the power of $2$ .

$m = \frac{7 \pm \sqrt{49 - 4 \cdot 5 \cdot - 5}}{2 \cdot 5}$

Step 4.1.2

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

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Step 4.1.2.1

Multiply $- 4$ by $5$ .

$m = \frac{7 \pm \sqrt{49 - 20 \cdot - 5}}{2 \cdot 5}$

Step 4.1.2.2

Multiply $- 20$ by $- 5$ .

$m = \frac{7 \pm \sqrt{49 + 100}}{2 \cdot 5}$

Step 4.1.3

Add $49$ and $100$ .

$m = \frac{7 \pm \sqrt{149}}{2 \cdot 5}$

Step 4.2

Multiply $2$ by $5$ .

$m = \frac{7 \pm \sqrt{149}}{10}$

Step 5

The final answer is the combination of both solutions.

$m = \frac{7 + \sqrt{149}}{10}, \frac{7 - \sqrt{149}}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = \frac{7 + \sqrt{149}}{10}, \frac{7 - \sqrt{149}}{10}$

Decimal Form:

$m = 1.92065556 \dots, - 0.52065556 \dots$