Finite Math Examples

$100 x^{2} + 60 x + 9$

Step 1

Set $100 x^{2} + 60 x + 9$ equal to $0$ .

$100 x^{2} + 60 x + 9 = 0$

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 $a = 100$ , $b = 60$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{- 60 \pm \sqrt{60^{2} - 4 \cdot (100 \cdot 9)}}{2 \cdot 100}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $60$ to the power of $2$ .

$x = \frac{- 60 \pm \sqrt{3600 - 4 \cdot 100 \cdot 9}}{2 \cdot 100}$

Step 4.1.2

Multiply $- 4 \cdot 100 \cdot 9$ .

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Step 4.1.2.1

Multiply $- 4$ by $100$ .

$x = \frac{- 60 \pm \sqrt{3600 - 400 \cdot 9}}{2 \cdot 100}$

Step 4.1.2.2

Multiply $- 400$ by $9$ .

$x = \frac{- 60 \pm \sqrt{3600 - 3600}}{2 \cdot 100}$

Step 4.1.3

Subtract $3600$ from $3600$ .

$x = \frac{- 60 \pm \sqrt{0}}{2 \cdot 100}$

Step 4.1.4

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

$x = \frac{- 60 \pm \sqrt{0^{2}}}{2 \cdot 100}$

Step 4.1.5

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

$x = \frac{- 60 \pm 0}{2 \cdot 100}$

Step 4.1.6

$- 60$ plus or minus $0$ is $- 60$ .

$x = \frac{- 60}{2 \cdot 100}$

Step 4.2

Multiply $2$ by $100$ .

$x = \frac{- 60}{200}$

Step 4.3

Cancel the common factor of $- 60$ and $200$ .

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Step 4.3.1

Factor $20$ out of $- 60$ .

$x = \frac{20 (- 3)}{200}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $20$ out of $200$ .

$x = \frac{20 \cdot - 3}{20 \cdot 10}$

Step 4.3.2.2

Cancel the common factor.

$x = \frac{20 \cdot - 3}{20 \cdot 10}$

Step 4.3.2.3

Rewrite the expression.

$x = \frac{- 3}{10}$

Step 4.4

Move the negative in front of the fraction.

$x = - \frac{3}{10}$

Step 5

The final answer is the combination of both solutions.

$x = - \frac{3}{10}$ Double roots