Algebra Examples

$5 m^{2} + 9 m = 126$

Step 1

Subtract $126$ from both sides of the equation.

$5 m^{2} + 9 m - 126 = 0$

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 $a = 5$ , $b = 9$ , and $c = - 126$ into the quadratic formula and solve for $m$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (5 \cdot - 126)}}{2 \cdot 5}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $9$ to the power of $2$ .

$m = \frac{- 9 \pm \sqrt{81 - 4 \cdot 5 \cdot - 126}}{2 \cdot 5}$

Step 4.1.2

Multiply $- 4 \cdot 5 \cdot - 126$ .

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Step 4.1.2.1

Multiply $- 4$ by $5$ .

$m = \frac{- 9 \pm \sqrt{81 - 20 \cdot - 126}}{2 \cdot 5}$

Step 4.1.2.2

Multiply $- 20$ by $- 126$ .

$m = \frac{- 9 \pm \sqrt{81 + 2520}}{2 \cdot 5}$

Step 4.1.3

Add $81$ and $2520$ .

$m = \frac{- 9 \pm \sqrt{2601}}{2 \cdot 5}$

Step 4.1.4

Rewrite $2601$ as $51^{2}$ .

$m = \frac{- 9 \pm \sqrt{51^{2}}}{2 \cdot 5}$

Step 4.1.5

Pull terms out from under the radical, assuming positive real numbers.

$m = \frac{- 9 \pm 51}{2 \cdot 5}$

Step 4.2

Multiply $2$ by $5$ .

$m = \frac{- 9 \pm 51}{10}$

Step 5

The final answer is the combination of both solutions.

$m = \frac{21}{5}, - 6$