Finite Math Examples

$t^{2} = - 12 - t$

Step 1

Add $t$ to both sides of the equation.

$t^{2} + t = - 12$

Step 2

Add $12$ to both sides of the equation.

$t^{2} + t + 12 = 0$

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 $a = 1$ , $b = 1$ , and $c = 12$ into the quadratic formula and solve for $t$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (1 \cdot 12)}}{2 \cdot 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

One to any power is one.

$t = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1 \cdot 12}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4 \cdot 1 \cdot 12$ .

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Step 5.1.2.1

Multiply $- 4$ by $1$ .

$t = \frac{- 1 \pm \sqrt{1 - 4 \cdot 12}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $12$ .

$t = \frac{- 1 \pm \sqrt{1 - 48}}{2 \cdot 1}$

Step 5.1.3

Subtract $48$ from $1$ .

$t = \frac{- 1 \pm \sqrt{- 47}}{2 \cdot 1}$

Step 5.1.4

Rewrite $- 47$ as $- 1 (47)$ .

$t = \frac{- 1 \pm \sqrt{- 1 \cdot 47}}{2 \cdot 1}$

Step 5.1.5

Rewrite $\sqrt{- 1 (47)}$ as $\sqrt{- 1} \cdot \sqrt{47}$ .

$t = \frac{- 1 \pm \sqrt{- 1} \cdot \sqrt{47}}{2 \cdot 1}$

Step 5.1.6

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

$t = \frac{- 1 \pm i \sqrt{47}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$t = \frac{- 1 \pm i \sqrt{47}}{2}$

Step 6

The final answer is the combination of both solutions.

$t = - \frac{1 - i \sqrt{47}}{2}, - \frac{1 + i \sqrt{47}}{2}$