Finite Math Examples

$0 = 3.51 x^{2} + 24.4 x - 8000000000000$

Step 1

Rewrite the equation as $3.51 x^{2} + 24.4 x - 8000000000000 = 0$ .

$3.51 x^{2} + 24.4 x - 8000000000000 = 0$

Step 2

Factor $0.01$ out of $3.51 x^{2} + 24.4 x - 8000000000000$ .

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Step 2.1

Factor $0.01$ out of $3.51 x^{2}$ .

$0.01 (351 x^{2}) + 24.4 x - 8000000000000 = 0$

Step 2.2

Factor $0.01$ out of $24.4 x$ .

$0.01 (351 x^{2}) + 0.01 (2440 x) - 8000000000000 = 0$

Step 2.3

Factor $0.01$ out of $- 8000000000000$ .

$0.01 (351 x^{2}) + 0.01 (2440 x) + 0.01 (- 800000000000000) = 0$

Step 2.4

Factor $0.01$ out of $0.01 (351 x^{2}) + 0.01 (2440 x)$ .

$0.01 (351 x^{2} + 2440 x) + 0.01 (- 800000000000000) = 0$

Step 2.5

Factor $0.01$ out of $0.01 (351 x^{2} + 2440 x) + 0.01 (- 800000000000000)$ .

$0.01 (351 x^{2} + 2440 x - 800000000000000) = 0$

Step 3

Divide each term in $0.01 (351 x^{2} + 2440 x - 800000000000000) = 0$ by $0.01$ and simplify.

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Step 3.1

Divide each term in $0.01 (351 x^{2} + 2440 x - 800000000000000) = 0$ by $0.01$ .

$\frac{0.01 (351 x^{2} + 2440 x - 800000000000000)}{0.01} = \frac{0}{0.01}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.01$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.01 (351 x^{2} + 2440 x - 800000000000000)}{0.01} = \frac{0}{0.01}$

Step 3.2.1.2

Divide $351 x^{2} + 2440 x - 800000000000000$ by $1$ .

$351 x^{2} + 2440 x - 800000000000000 = \frac{0}{0.01}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $0.01$ .

$351 x^{2} + 2440 x - 800000000000000 = 0$

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 $a = 351$ , $b = 2440$ , and $c = - 800000000000000$ into the quadratic formula and solve for $x$ .

$\frac{- 2440 \pm \sqrt{2440^{2} - 4 \cdot (351 \cdot - 800000000000000)}}{2 \cdot 351}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Raise $2440$ to the power of $2$ .

$x = \frac{- 2440 \pm \sqrt{5953600 - 4 \cdot 351 \cdot - 800000000000000}}{2 \cdot 351}$

Step 6.1.2

Multiply $- 4 \cdot 351 \cdot - 800000000000000$ .

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Step 6.1.2.1

Multiply $- 4$ by $351$ .

$x = \frac{- 2440 \pm \sqrt{5953600 - 1404 \cdot - 800000000000000}}{2 \cdot 351}$

Step 6.1.2.2

Multiply $- 1404$ by $- 800000000000000$ .

$x = \frac{- 2440 \pm \sqrt{5953600 + 1123200000000000000}}{2 \cdot 351}$

Step 6.1.3

Add $5953600$ and $1123200000000000000$ .

$x = \frac{- 2440 \pm \sqrt{1123200000005953600}}{2 \cdot 351}$

Step 6.2

Multiply $2$ by $351$ .

$x = \frac{- 2440 \pm \sqrt{1123200000005953600}}{702}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 2440 \pm \sqrt{1123200000005953600}}{702}$

Decimal Form:

$x = 1509699.23641332, - 1509706.18798027$

Step 8