Finite Math Examples

$8.25 x^{2} + 2.99 x = 4.66$

Step 1

Subtract $4.66$ from both sides of the equation.

$8.25 x^{2} + 2.99 x - 4.66 = 0$

Step 2

Factor $0.01$ out of $8.25 x^{2} + 2.99 x - 4.66$ .

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Step 2.1

Factor $0.01$ out of $8.25 x^{2}$ .

$0.01 (825 x^{2}) + 2.99 x - 4.66 = 0$

Step 2.2

Factor $0.01$ out of $2.99 x$ .

$0.01 (825 x^{2}) + 0.01 (299 x) - 4.66 = 0$

Step 2.3

Factor $0.01$ out of $- 4.66$ .

$0.01 (825 x^{2}) + 0.01 (299 x) + 0.01 (- 466) = 0$

Step 2.4

Factor $0.01$ out of $0.01 (825 x^{2}) + 0.01 (299 x)$ .

$0.01 (825 x^{2} + 299 x) + 0.01 (- 466) = 0$

Step 2.5

Factor $0.01$ out of $0.01 (825 x^{2} + 299 x) + 0.01 (- 466)$ .

$0.01 (825 x^{2} + 299 x - 466) = 0$

Step 3

Divide each term in $0.01 (825 x^{2} + 299 x - 466) = 0$ by $0.01$ and simplify.

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Step 3.1

Divide each term in $0.01 (825 x^{2} + 299 x - 466) = 0$ by $0.01$ .

$\frac{0.01 (825 x^{2} + 299 x - 466)}{0.01} = \frac{0}{0.01}$

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.

$\frac{0.01 (825 x^{2} + 299 x - 466)}{0.01} = \frac{0}{0.01}$

Step 3.2.1.2

Divide $825 x^{2} + 299 x - 466$ by $1$ .

$825 x^{2} + 299 x - 466 = \frac{0}{0.01}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $0.01$ .

$825 x^{2} + 299 x - 466 = 0$

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 $a = 825$ , $b = 299$ , and $c = - 466$ into the quadratic formula and solve for $x$ .

$\frac{- 299 \pm \sqrt{299^{2} - 4 \cdot (825 \cdot - 466)}}{2 \cdot 825}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Raise $299$ to the power of $2$ .

$x = \frac{- 299 \pm \sqrt{89401 - 4 \cdot 825 \cdot - 466}}{2 \cdot 825}$

Step 6.1.2

Multiply $- 4 \cdot 825 \cdot - 466$ .

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Step 6.1.2.1

Multiply $- 4$ by $825$ .

$x = \frac{- 299 \pm \sqrt{89401 - 3300 \cdot - 466}}{2 \cdot 825}$

Step 6.1.2.2

Multiply $- 3300$ by $- 466$ .

$x = \frac{- 299 \pm \sqrt{89401 + 1537800}}{2 \cdot 825}$

Step 6.1.3

Add $89401$ and $1537800$ .

$x = \frac{- 299 \pm \sqrt{1627201}}{2 \cdot 825}$

Step 6.2

Multiply $2$ by $825$ .

$x = \frac{- 299 \pm \sqrt{1627201}}{1650}$

Step 7

The final answer is the combination of both solutions.

$x = - \frac{299 - \sqrt{1627201}}{1650}, - \frac{299 + \sqrt{1627201}}{1650}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{299 - \sqrt{1627201}}{1650}, - \frac{299 + \sqrt{1627201}}{1650}$

Decimal Form:

$x = 0.59188962 \dots, - 0.95431387 \dots$