Finite Math Examples

$5 x^{2} + 5 x = - 1$

Step 1

Add $1$ to both sides of the equation.

$5 x^{2} + 5 x + 1 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 5$ , $b = 5$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (5 \cdot 1)}}{2 \cdot 5}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $5$ to the power of $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 5 \cdot 1}}{2 \cdot 5}$

Step 4.1.2

Multiply $- 4 \cdot 5 \cdot 1$ .

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Step 4.1.2.1

Multiply $- 4$ by $5$ .

$x = \frac{- 5 \pm \sqrt{25 - 20 \cdot 1}}{2 \cdot 5}$

Step 4.1.2.2

Multiply $- 20$ by $1$ .

$x = \frac{- 5 \pm \sqrt{25 - 20}}{2 \cdot 5}$

Step 4.1.3

Subtract $20$ from $25$ .

$x = \frac{- 5 \pm \sqrt{5}}{2 \cdot 5}$

Step 4.2

Multiply $2$ by $5$ .

$x = \frac{- 5 \pm \sqrt{5}}{10}$

Step 5

The final answer is the combination of both solutions.

$x = - \frac{5 - \sqrt{5}}{10}, - \frac{5 + \sqrt{5}}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5 - \sqrt{5}}{10}, - \frac{5 + \sqrt{5}}{10}$

Decimal Form:

$x = - 0.27639320 \dots, - 0.72360679 \dots$