Solve Using the Quadratic Formula 1/4m^2+3/5m=-1/4

$\frac{1}{4} m^{2} + \frac{3}{5} m = - \frac{1}{4}$

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

Simplify the left side.

Simplify each term.

Combine $\frac{1}{4}$ and $m^{2}$ .

$\frac{m^{2}}{4} + \frac{3}{5} m = - \frac{1}{4}$

Combine $\frac{3}{5}$ and $m$ .

$\frac{m^{2}}{4} + \frac{3 m}{5} = - \frac{1}{4}$

Add $\frac{1}{4}$ to both sides of the equation.

$\frac{m^{2}}{4} + \frac{3 m}{5} + \frac{1}{4} = 0$

Multiply through by the least common denominator $20$ , then simplify.

Apply the distributive property.

$20 (\frac{m^{2}}{4}) + 20 (\frac{3 m}{5}) + 20 (\frac{1}{4}) = 0$

Simplify.

Cancel the common factor of $4$ .

Factor $4$ out of $20$ .

$4 (5) (\frac{m^{2}}{4}) + 20 (\frac{3 m}{5}) + 20 (\frac{1}{4}) = 0$

Cancel the common factor.

$4 \cdot (5 (\frac{m^{2}}{4})) + 20 (\frac{3 m}{5}) + 20 (\frac{1}{4}) = 0$

Rewrite the expression.

$5 m^{2} + 20 (\frac{3 m}{5}) + 20 (\frac{1}{4}) = 0$

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$5 m^{2} + 5 (4) (\frac{3 m}{5}) + 20 (\frac{1}{4}) = 0$

Cancel the common factor.

$5 m^{2} + 5 \cdot (4 (\frac{3 m}{5})) + 20 (\frac{1}{4}) = 0$

Rewrite the expression.

$5 m^{2} + 4 (3 m) + 20 (\frac{1}{4}) = 0$

Multiply $3$ by $4$ .

$5 m^{2} + 12 m + 20 (\frac{1}{4}) = 0$

Cancel the common factor of $4$ .

Factor $4$ out of $20$ .

$5 m^{2} + 12 m + 4 (5) (\frac{1}{4}) = 0$

Cancel the common factor.

$5 m^{2} + 12 m + 4 \cdot (5 (\frac{1}{4})) = 0$

Rewrite the expression.

$5 m^{2} + 12 m + 5 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 5$ , $b = 12$ , and $c = 5$ into the quadratic formula and solve for $m$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (5 \cdot 5)}}{2 \cdot 5}$

Simplify.

Simplify the numerator.

Raise $12$ to the power of $2$ .

$m = \frac{- 12 \pm \sqrt{144 - 4 \cdot 5 \cdot 5}}{2 \cdot 5}$

Multiply $- 4$ by $5$ .

$m = \frac{- 12 \pm \sqrt{144 - 20 \cdot 5}}{2 \cdot 5}$

Multiply $- 20$ by $5$ .

$m = \frac{- 12 \pm \sqrt{144 - 100}}{2 \cdot 5}$

Subtract $100$ from $144$ .

$m = \frac{- 12 \pm \sqrt{44}}{2 \cdot 5}$

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$m = \frac{- 12 \pm \sqrt{4 (11)}}{2 \cdot 5}$

Rewrite $4$ as $2^{2}$ .

$m = \frac{- 12 \pm \sqrt{2^{2} \cdot 11}}{2 \cdot 5}$

Pull terms out from under the radical.

$m = \frac{- 12 \pm 2 \sqrt{11}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$m = \frac{- 12 \pm 2 \sqrt{11}}{10}$

Simplify $\frac{- 12 \pm 2 \sqrt{11}}{10}$ .

$m = \frac{- 6 \pm \sqrt{11}}{5}$

The result can be shown in multiple forms.

Exact Form:

$m = \frac{- 6 \pm \sqrt{11}}{5}$

Decimal Form:

$m = - 0.53667504 \dots, - 1.86332495 \dots$

Solve Using the Quadratic Formula 1/4m^2+3/5m=-1/4

Related Questions

Support LCMGCF.com by disabling your adblocker.