Finite Math Examples

$81 x^{2} + 90 x + 25$

Step 1

Set $81 x^{2} + 90 x + 25$ equal to $0$ .

$81 x^{2} + 90 x + 25 = 0$

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 $a = 81$ , $b = 90$ , and $c = 25$ into the quadratic formula and solve for $x$ .

$\frac{- 90 \pm \sqrt{90^{2} - 4 \cdot (81 \cdot 25)}}{2 \cdot 81}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $90$ to the power of $2$ .

$x = \frac{- 90 \pm \sqrt{8100 - 4 \cdot 81 \cdot 25}}{2 \cdot 81}$

Step 4.1.2

Multiply $- 4 \cdot 81 \cdot 25$ .

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Step 4.1.2.1

Multiply $- 4$ by $81$ .

$x = \frac{- 90 \pm \sqrt{8100 - 324 \cdot 25}}{2 \cdot 81}$

Step 4.1.2.2

Multiply $- 324$ by $25$ .

$x = \frac{- 90 \pm \sqrt{8100 - 8100}}{2 \cdot 81}$

Step 4.1.3

Subtract $8100$ from $8100$ .

$x = \frac{- 90 \pm \sqrt{0}}{2 \cdot 81}$

Step 4.1.4

Rewrite $0$ as $0^{2}$ .

$x = \frac{- 90 \pm \sqrt{0^{2}}}{2 \cdot 81}$

Step 4.1.5

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 90 \pm 0}{2 \cdot 81}$

Step 4.1.6

$- 90$ plus or minus $0$ is $- 90$ .

$x = \frac{- 90}{2 \cdot 81}$

Step 4.2

Multiply $2$ by $81$ .

$x = \frac{- 90}{162}$

Step 4.3

Cancel the common factor of $- 90$ and $162$ .

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Step 4.3.1

Factor $18$ out of $- 90$ .

$x = \frac{18 (- 5)}{162}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $18$ out of $162$ .

$x = \frac{18 \cdot - 5}{18 \cdot 9}$

Step 4.3.2.2

Cancel the common factor.

$x = \frac{18 \cdot - 5}{18 \cdot 9}$

Step 4.3.2.3

Rewrite the expression.

$x = \frac{- 5}{9}$

Step 4.4

Move the negative in front of the fraction.

$x = - \frac{5}{9}$

Step 5

The final answer is the combination of both solutions.

$x = - \frac{5}{9}$ Double roots