Basic Math Examples

$78 = s \cdot (s + 1)$

Step 1

Rewrite the equation as $s \cdot (s + 1) = 78$ .

$s \cdot (s + 1) = 78$

Step 2

Simplify $s \cdot (s + 1)$ .

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Step 2.1

Apply the distributive property.

$s \cdot s + s \cdot 1 = 78$

Step 2.2

Simplify the expression.

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Step 2.2.1

Multiply $s$ by $s$ .

$s^{2} + s \cdot 1 = 78$

Step 2.2.2

Multiply $s$ by $1$ .

$s^{2} + s = 78$

Step 3

Subtract $78$ from both sides of the equation.

$s^{2} + s - 78 = 0$

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = 1$ , $b = 1$ , and $c = - 78$ into the quadratic formula and solve for $s$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (1 \cdot - 78)}}{2 \cdot 1}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

One to any power is one.

$s = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1 \cdot - 78}}{2 \cdot 1}$

Step 6.1.2

Multiply $- 4 \cdot 1 \cdot - 78$ .

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Step 6.1.2.1

Multiply $- 4$ by $1$ .

$s = \frac{- 1 \pm \sqrt{1 - 4 \cdot - 78}}{2 \cdot 1}$

Step 6.1.2.2

Multiply $- 4$ by $- 78$ .

$s = \frac{- 1 \pm \sqrt{1 + 312}}{2 \cdot 1}$

Step 6.1.3

Add $1$ and $312$ .

$s = \frac{- 1 \pm \sqrt{313}}{2 \cdot 1}$

Step 6.2

Multiply $2$ by $1$ .

$s = \frac{- 1 \pm \sqrt{313}}{2}$

Step 7

The final answer is the combination of both solutions.

$s = - \frac{1 - \sqrt{313}}{2}, - \frac{1 + \sqrt{313}}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$s = - \frac{1 - \sqrt{313}}{2}, - \frac{1 + \sqrt{313}}{2}$

Decimal Form:

$s = 8.34590300 \dots, - 9.34590300 \dots$