Finite Math Examples

$25 = \frac{1}{2} q^{2} + 30$

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

$25 = \frac{q^{2}}{2} + 30$

Step 1.2

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

Tap for more steps...

Step 1.2.1

Subtract $\frac{q^{2}}{2}$ from both sides of the equation.

$25 - \frac{q^{2}}{2} = 30$

Step 1.2.2

Subtract $30$ from both sides of the equation.

$25 - \frac{q^{2}}{2} - 30 = 0$

Step 1.3

Subtract $30$ from $25$ .

$- \frac{q^{2}}{2} - 5 = 0$

Step 2

Multiply through by the least common denominator $2$ , then simplify.

Tap for more steps...

Step 2.1

Apply the distributive property.

$2 (- \frac{q^{2}}{2}) + 2 \cdot - 5 = 0$

Step 2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1

Move the leading negative in $- \frac{q^{2}}{2}$ into the numerator.

$2 (\frac{- q^{2}}{2}) + 2 \cdot - 5 = 0$

Step 2.2.2

Cancel the common factor.

$2 (\frac{- q^{2}}{2}) + 2 \cdot - 5 = 0$

Step 2.2.3

Rewrite the expression.

$- q^{2} + 2 \cdot - 5 = 0$

Step 2.3

Multiply $2$ by $- 5$ .

$- q^{2} - 10 = 0$

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 $c = - 10$ into the quadratic formula and solve for $q$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 1 \cdot - 10)}}{2 \cdot - 1}$

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 $0$ .

$q = \frac{0 \pm \sqrt{0 - 4 \cdot - 1 \cdot - 10}}{2 \cdot - 1}$

Step 5.1.2

Multiply $- 4 \cdot - 1 \cdot - 10$ .

Tap for more steps...

Step 5.1.2.1

Multiply $- 4$ by $- 1$ .

$q = \frac{0 \pm \sqrt{0 + 4 \cdot - 10}}{2 \cdot - 1}$

Step 5.1.2.2

Multiply $4$ by $- 10$ .

$q = \frac{0 \pm \sqrt{0 - 40}}{2 \cdot - 1}$

Step 5.1.3

Subtract $40$ from $0$ .

$q = \frac{0 \pm \sqrt{- 40}}{2 \cdot - 1}$

Step 5.1.4

Rewrite $- 40$ as $- 1 (40)$ .

$q = \frac{0 \pm \sqrt{- 1 \cdot 40}}{2 \cdot - 1}$

Step 5.1.5

Rewrite $\sqrt{- 1 (40)}$ as $\sqrt{- 1} \cdot \sqrt{40}$ .

$q = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{40}}{2 \cdot - 1}$

Step 5.1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$q = \frac{0 \pm i \cdot \sqrt{40}}{2 \cdot - 1}$

Step 5.1.7

Rewrite $40$ as $2^{2} \cdot 10$ .

Tap for more steps...

Step 5.1.7.1

Factor $4$ out of $40$ .

$q = \frac{0 \pm i \cdot \sqrt{4 (10)}}{2 \cdot - 1}$

Step 5.1.7.2

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

$q = \frac{0 \pm i \cdot \sqrt{2^{2} \cdot 10}}{2 \cdot - 1}$

Step 5.1.8

Pull terms out from under the radical.

$q = \frac{0 \pm i \cdot (2 \sqrt{10})}{2 \cdot - 1}$

Step 5.1.9

Move $2$ to the left of $i$ .

$q = \frac{0 \pm 2 i \sqrt{10}}{2 \cdot - 1}$

Step 5.2

Multiply $2$ by $- 1$ .

$q = \frac{0 \pm 2 i \sqrt{10}}{- 2}$

Step 5.3

Simplify $\frac{0 \pm 2 i \sqrt{10}}{- 2}$ .

$q = \pm i \sqrt{10}$