Finite Math Examples

$2.6 + 3.3 x - 0.2 x^{2} = 0$

Step 1

Factor $- 0.1$ out of $2.6 + 3.3 x - 0.2 x^{2}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move $2.6$ .

$3.3 x - 0.2 x^{2} + 2.6 = 0$

Step 1.1.2

Reorder $3.3 x$ and $- 0.2 x^{2}$ .

$- 0.2 x^{2} + 3.3 x + 2.6 = 0$

Step 1.2

Factor $- 0.1$ out of $- 0.2 x^{2}$ .

$- 0.1 (2 x^{2}) + 3.3 x + 2.6 = 0$

Step 1.3

Factor $- 0.1$ out of $3.3 x$ .

$- 0.1 (2 x^{2}) - 0.1 (- 33 x) + 2.6 = 0$

Step 1.4

Factor $- 0.1$ out of $2.6$ .

$- 0.1 (2 x^{2}) - 0.1 (- 33 x) - 0.1 \cdot - 26 = 0$

Step 1.5

Factor $- 0.1$ out of $- 0.1 (2 x^{2}) - 0.1 (- 33 x)$ .

$- 0.1 (2 x^{2} - 33 x) - 0.1 \cdot - 26 = 0$

Step 1.6

Factor $- 0.1$ out of $- 0.1 (2 x^{2} - 33 x) - 0.1 (- 26)$ .

$- 0.1 (2 x^{2} - 33 x - 26) = 0$

Step 2

Divide each term in $- 0.1 (2 x^{2} - 33 x - 26) = 0$ by $- 0.1$ and simplify.

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Step 2.1

Divide each term in $- 0.1 (2 x^{2} - 33 x - 26) = 0$ by $- 0.1$ .

$\frac{- 0.1 (2 x^{2} - 33 x - 26)}{- 0.1} = \frac{0}{- 0.1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 0.1$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 0.1 (2 x^{2} - 33 x - 26)}{- 0.1} = \frac{0}{- 0.1}$

Step 2.2.1.2

Divide $2 x^{2} - 33 x - 26$ by $1$ .

$2 x^{2} - 33 x - 26 = \frac{0}{- 0.1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $- 0.1$ .

$2 x^{2} - 33 x - 26 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 2$ , $b = - 33$ , and $c = - 26$ into the quadratic formula and solve for $x$ .

$\frac{33 \pm \sqrt{{(- 33)}^{2} - 4 \cdot (2 \cdot - 26)}}{2 \cdot 2}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $- 33$ to the power of $2$ .

$x = \frac{33 \pm \sqrt{1089 - 4 \cdot 2 \cdot - 26}}{2 \cdot 2}$

Step 5.1.2

Multiply $- 4 \cdot 2 \cdot - 26$ .

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Step 5.1.2.1

Multiply $- 4$ by $2$ .

$x = \frac{33 \pm \sqrt{1089 - 8 \cdot - 26}}{2 \cdot 2}$

Step 5.1.2.2

Multiply $- 8$ by $- 26$ .

$x = \frac{33 \pm \sqrt{1089 + 208}}{2 \cdot 2}$

Step 5.1.3

Add $1089$ and $208$ .

$x = \frac{33 \pm \sqrt{1297}}{2 \cdot 2}$

Step 5.2

Multiply $2$ by $2$ .

$x = \frac{33 \pm \sqrt{1297}}{4}$

Step 6

The final answer is the combination of both solutions.

$x = \frac{33 + \sqrt{1297}}{4}, \frac{33 - \sqrt{1297}}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{33 + \sqrt{1297}}{4}, \frac{33 - \sqrt{1297}}{4}$

Decimal Form:

$x = 17.25347155 \dots, - 0.75347155 \dots$