Finite Math Examples

$25 t^{2} - 20 t + 4 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 25$ , $b = - 20$ , and $c = 4$ into the quadratic formula and solve for $t$ .

$\frac{20 \pm \sqrt{{(- 20)}^{2} - 4 \cdot (25 \cdot 4)}}{2 \cdot 25}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $- 20$ to the power of $2$ .

$t = \frac{20 \pm \sqrt{400 - 4 \cdot 25 \cdot 4}}{2 \cdot 25}$

Step 3.1.2

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

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Step 3.1.2.1

Multiply $- 4$ by $25$ .

$t = \frac{20 \pm \sqrt{400 - 100 \cdot 4}}{2 \cdot 25}$

Step 3.1.2.2

Multiply $- 100$ by $4$ .

$t = \frac{20 \pm \sqrt{400 - 400}}{2 \cdot 25}$

Step 3.1.3

Subtract $400$ from $400$ .

$t = \frac{20 \pm \sqrt{0}}{2 \cdot 25}$

Step 3.1.4

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

$t = \frac{20 \pm \sqrt{0^{2}}}{2 \cdot 25}$

Step 3.1.5

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

$t = \frac{20 \pm 0}{2 \cdot 25}$

Step 3.1.6

$20$ plus or minus $0$ is $20$ .

$t = \frac{20}{2 \cdot 25}$

Step 3.2

Multiply $2$ by $25$ .

$t = \frac{20}{50}$

Step 3.3

Cancel the common factor of $20$ and $50$ .

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Step 3.3.1

Factor $10$ out of $20$ .

$t = \frac{10 (2)}{50}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $10$ out of $50$ .

$t = \frac{10 \cdot 2}{10 \cdot 5}$

Step 3.3.2.2

Cancel the common factor.

$t = \frac{10 \cdot 2}{10 \cdot 5}$

Step 3.3.2.3

Rewrite the expression.

$t = \frac{2}{5}$

Step 4

The final answer is the combination of both solutions.

$t = \frac{2}{5}$ Double roots