Finite Math Examples

$14 m^{2} + 1 = 6 m^{2} - 7 m$

Step 1

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

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Step 1.1

Move all the expressions to the left side of the equation.

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Step 1.1.1

Subtract $6 m^{2}$ from both sides of the equation.

$14 m^{2} + 1 - 6 m^{2} = - 7 m$

Step 1.1.2

Add $7 m$ to both sides of the equation.

$14 m^{2} + 1 - 6 m^{2} + 7 m = 0$

Step 1.2

Subtract $6 m^{2}$ from $14 m^{2}$ .

$8 m^{2} + 1 + 7 m = 0$

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 $a = 8$ , $b = 7$ , and $c = 1$ into the quadratic formula and solve for $m$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (8 \cdot 1)}}{2 \cdot 8}$

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 $2$ .

$m = \frac{- 7 \pm \sqrt{49 - 4 \cdot 8 \cdot 1}}{2 \cdot 8}$

Step 4.1.2

Multiply $- 4 \cdot 8 \cdot 1$ .

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Step 4.1.2.1

Multiply $- 4$ by $8$ .

$m = \frac{- 7 \pm \sqrt{49 - 32 \cdot 1}}{2 \cdot 8}$

Step 4.1.2.2

Multiply $- 32$ by $1$ .

$m = \frac{- 7 \pm \sqrt{49 - 32}}{2 \cdot 8}$

Step 4.1.3

Subtract $32$ from $49$ .

$m = \frac{- 7 \pm \sqrt{17}}{2 \cdot 8}$

Step 4.2

Multiply $2$ by $8$ .

$m = \frac{- 7 \pm \sqrt{17}}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$m = \frac{- 7 \pm \sqrt{17}}{16}$

Decimal Form:

$m = - 0.17980589 \dots, - 0.69519410 \dots$