Finite Math Examples

$3.51 x^{2} + 24.4 x - 8220$

Step 1

Set $3.51 x^{2} + 24.4 x - 8220$ equal to $0$ .

$3.51 x^{2} + 24.4 x - 8220 = 0$

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 $a = 3.51$ , $b = 24.4$ , and $c = - 8220$ into the quadratic formula and solve for $x$ .

$\frac{- 24.4 \pm \sqrt{{24.4}^{2} - 4 \cdot (3.51 \cdot - 8220)}}{2 \cdot 3.51}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $24.4$ to the power of $2$ .

$x = \frac{- 24.4 \pm \sqrt{595.36 - 4 \cdot 3.51 \cdot - 8220}}{2 \cdot 3.51}$

Step 4.1.2

Multiply $- 4 \cdot 3.51 \cdot - 8220$ .

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Step 4.1.2.1

Multiply $- 4$ by $3.51$ .

$x = \frac{- 24.4 \pm \sqrt{595.36 - 14.04 \cdot - 8220}}{2 \cdot 3.51}$

Step 4.1.2.2

Multiply $- 14.04$ by $- 8220$ .

$x = \frac{- 24.4 \pm \sqrt{595.36 + 115408.8}}{2 \cdot 3.51}$

Step 4.1.3

Add $595.36$ and $115408.8$ .

$x = \frac{- 24.4 \pm \sqrt{116004.16}}{2 \cdot 3.51}$

Step 4.2

Multiply $2$ by $3.51$ .

$x = \frac{- 24.4 \pm \sqrt{116004.16}}{7.02}$

Step 4.3

Simplify $\frac{- 24.4 \pm \sqrt{116004.16}}{7.02}$ .

$x = \frac{- 1220 \pm 50 \sqrt{116004.16}}{351}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 1220 \pm 50 \sqrt{116004.16}}{351}$

Decimal Form:

$x = 45.04185674 \dots, - 51.99342369 \dots$