Finite Math Examples

$- 15 = - \frac{1}{3} q^{2}$

Step 1

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

Tap for more steps...

Step 1.1

Simplify the right side.

Tap for more steps...

Step 1.1.1

Combine $q^{2}$ and $\frac{1}{3}$ .

$- 15 = - \frac{q^{2}}{3}$

Step 1.2

Add $\frac{q^{2}}{3}$ to both sides of the equation.

$- 15 + \frac{q^{2}}{3} = 0$

Step 2

Multiply through by the least common denominator $3$ , then simplify.

Tap for more steps...

Step 2.1

Apply the distributive property.

$3 \cdot - 15 + 3 (\frac{q^{2}}{3}) = 0$

Step 2.2

Multiply $3$ by $- 15$ .

$- 45 + 3 (\frac{q^{2}}{3}) = 0$

Step 2.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.3.1

Cancel the common factor.

$- 45 + 3 (\frac{q^{2}}{3}) = 0$

Step 2.3.2

Rewrite the expression.

$- 45 + q^{2} = 0$

Step 2.4

Reorder $- 45$ and $q^{2}$ .

$q^{2} - 45 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 1$ , $b = 0$ , and $c = - 45$ into the quadratic formula and solve for $q$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 45)}}{2 \cdot 1}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

Raising $0$ to any positive power yields $0$ .

$q = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 45}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4 \cdot 1 \cdot - 45$ .

Tap for more steps...

Step 5.1.2.1

Multiply $- 4$ by $1$ .

$q = \frac{0 \pm \sqrt{0 - 4 \cdot - 45}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $- 45$ .

$q = \frac{0 \pm \sqrt{0 + 180}}{2 \cdot 1}$

Step 5.1.3

Add $0$ and $180$ .

$q = \frac{0 \pm \sqrt{180}}{2 \cdot 1}$

Step 5.1.4

Rewrite $180$ as $6^{2} \cdot 5$ .

Tap for more steps...

Step 5.1.4.1

Factor $36$ out of $180$ .

$q = \frac{0 \pm \sqrt{36 (5)}}{2 \cdot 1}$

Step 5.1.4.2

Rewrite $36$ as $6^{2}$ .

$q = \frac{0 \pm \sqrt{6^{2} \cdot 5}}{2 \cdot 1}$

Step 5.1.5

Pull terms out from under the radical.

$q = \frac{0 \pm 6 \sqrt{5}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$q = \frac{0 \pm 6 \sqrt{5}}{2}$

Step 5.3

Simplify $\frac{0 \pm 6 \sqrt{5}}{2}$ .

$q = \pm 3 \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$q = \pm 3 \sqrt{5}$

Decimal Form:

$q = 6.70820393 \dots, - 6.70820393 \dots$