Pre-Algebra Examples

$2 m^{2} - 7 m - 13 = - 10$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Add $10$ to both sides of the equation.

$2 m^{2} - 7 m - 13 + 10 = 0$

Step 1.2

Add $- 13$ and $10$ .

$2 m^{2} - 7 m - 3 = 0$

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 $a = 2$ , $b = - 7$ , and $c = - 3$ into the quadratic formula and solve for $m$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (2 \cdot - 3)}}{2 \cdot 2}$

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 $2$ .

$m = \frac{7 \pm \sqrt{49 - 4 \cdot 2 \cdot - 3}}{2 \cdot 2}$

Step 4.1.2

Multiply $- 4 \cdot 2 \cdot - 3$ .

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Step 4.1.2.1

Multiply $- 4$ by $2$ .

$m = \frac{7 \pm \sqrt{49 - 8 \cdot - 3}}{2 \cdot 2}$

Step 4.1.2.2

Multiply $- 8$ by $- 3$ .

$m = \frac{7 \pm \sqrt{49 + 24}}{2 \cdot 2}$

Step 4.1.3

Add $49$ and $24$ .

$m = \frac{7 \pm \sqrt{73}}{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$m = \frac{7 \pm \sqrt{73}}{4}$

Step 5

The final answer is the combination of both solutions.

$m = \frac{7 + \sqrt{73}}{4}, \frac{7 - \sqrt{73}}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = \frac{7 + \sqrt{73}}{4}, \frac{7 - \sqrt{73}}{4}$

Decimal Form:

$m = 3.88600093 \dots, - 0.38600093 \dots$