Basic Math Examples

$s^{2} - 14 s + 74 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 1$ , $b = - 14$ , and $c = 74$ into the quadratic formula and solve for $s$ .

$\frac{14 \pm \sqrt{{(- 14)}^{2} - 4 \cdot (1 \cdot 74)}}{2 \cdot 1}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $- 14$ to the power of $2$ .

$s = \frac{14 \pm \sqrt{196 - 4 \cdot 1 \cdot 74}}{2 \cdot 1}$

Step 3.1.2

Multiply $- 4 \cdot 1 \cdot 74$ .

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Step 3.1.2.1

Multiply $- 4$ by $1$ .

$s = \frac{14 \pm \sqrt{196 - 4 \cdot 74}}{2 \cdot 1}$

Step 3.1.2.2

Multiply $- 4$ by $74$ .

$s = \frac{14 \pm \sqrt{196 - 296}}{2 \cdot 1}$

Step 3.1.3

Subtract $296$ from $196$ .

$s = \frac{14 \pm \sqrt{- 100}}{2 \cdot 1}$

Step 3.1.4

Rewrite $- 100$ as $- 1 (100)$ .

$s = \frac{14 \pm \sqrt{- 1 \cdot 100}}{2 \cdot 1}$

Step 3.1.5

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$s = \frac{14 \pm \sqrt{- 1} \cdot \sqrt{100}}{2 \cdot 1}$

Step 3.1.6

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

$s = \frac{14 \pm i \cdot \sqrt{100}}{2 \cdot 1}$

Step 3.1.7

Rewrite $100$ as $10^{2}$ .

$s = \frac{14 \pm i \cdot \sqrt{10^{2}}}{2 \cdot 1}$

Step 3.1.8

Pull terms out from under the radical, assuming positive real numbers.

$s = \frac{14 \pm i \cdot 10}{2 \cdot 1}$

Step 3.1.9

Move $10$ to the left of $i$ .

$s = \frac{14 \pm 10 i}{2 \cdot 1}$

Step 3.2

Multiply $2$ by $1$ .

$s = \frac{14 \pm 10 i}{2}$

Step 3.3

Simplify $\frac{14 \pm 10 i}{2}$ .

$s = 7 \pm 5 i$

Step 4

The final answer is the combination of both solutions.

$s = 7 + 5 i, 7 - 5 i$