Algebra Examples

$- 2.7 t^{2} + 50 t + 6.5$

Step 1

Set $- 2.7 t^{2} + 50 t + 6.5$ equal to $0$ .

$- 2.7 t^{2} + 50 t + 6.5 = 0$

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 $a = - 2.7$ , $b = 50$ , and $c = 6.5$ into the quadratic formula and solve for $t$ .

$\frac{- 50 \pm \sqrt{50^{2} - 4 \cdot (- 2.7 \cdot 6.5)}}{2 \cdot - 2.7}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $50$ to the power of $2$ .

$t = \frac{- 50 \pm \sqrt{2500 - 4 \cdot - 2.7 \cdot 6.5}}{2 \cdot - 2.7}$

Step 4.1.2

Multiply $- 4 \cdot - 2.7 \cdot 6.5$ .

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Step 4.1.2.1

Multiply $- 4$ by $- 2.7$ .

$t = \frac{- 50 \pm \sqrt{2500 + 10.8 \cdot 6.5}}{2 \cdot - 2.7}$

Step 4.1.2.2

Multiply $10.8$ by $6.5$ .

$t = \frac{- 50 \pm \sqrt{2500 + 70.2}}{2 \cdot - 2.7}$

Step 4.1.3

Add $2500$ and $70.2$ .

$t = \frac{- 50 \pm \sqrt{2570.2}}{2 \cdot - 2.7}$

Step 4.2

Multiply $2$ by $- 2.7$ .

$t = \frac{- 50 \pm \sqrt{2570.2}}{- 5.4}$

Step 4.3

Simplify $\frac{- 50 \pm \sqrt{2570.2}}{- 5.4}$ .

$t = \frac{250 \pm 5 \sqrt{2570.2}}{27}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{250 \pm 5 \sqrt{2570.2}}{27}$

Decimal Form:

$t = 18.64761851 \dots, - 0.12909999 \dots$