Basic Math Examples

$300 = 4.9 t^{2} + 5 t$

Step 1

Rewrite the equation as $4.9 t^{2} + 5 t = 300$ .

$4.9 t^{2} + 5 t = 300$

Step 2

Subtract $300$ from both sides of the equation.

$4.9 t^{2} + 5 t - 300 = 0$

Step 3

Factor $0.1$ out of $4.9 t^{2} + 5 t - 300$ .

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Step 3.1

Factor $0.1$ out of $4.9 t^{2}$ .

$0.1 (49 t^{2}) + 5 t - 300 = 0$

Step 3.2

Factor $0.1$ out of $5 t$ .

$0.1 (49 t^{2}) + 0.1 (50 t) - 300 = 0$

Step 3.3

Factor $0.1$ out of $- 300$ .

$0.1 (49 t^{2}) + 0.1 (50 t) + 0.1 (- 3000) = 0$

Step 3.4

Factor $0.1$ out of $0.1 (49 t^{2}) + 0.1 (50 t)$ .

$0.1 (49 t^{2} + 50 t) + 0.1 (- 3000) = 0$

Step 3.5

Factor $0.1$ out of $0.1 (49 t^{2} + 50 t) + 0.1 (- 3000)$ .

$0.1 (49 t^{2} + 50 t - 3000) = 0$

Step 4

Divide each term in $0.1 (49 t^{2} + 50 t - 3000) = 0$ by $0.1$ and simplify.

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Step 4.1

Divide each term in $0.1 (49 t^{2} + 50 t - 3000) = 0$ by $0.1$ .

$\frac{0.1 (49 t^{2} + 50 t - 3000)}{0.1} = \frac{0}{0.1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $0.1$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{0.1 (49 t^{2} + 50 t - 3000)}{0.1} = \frac{0}{0.1}$

Step 4.2.1.2

Divide $49 t^{2} + 50 t - 3000$ by $1$ .

$49 t^{2} + 50 t - 3000 = \frac{0}{0.1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $0.1$ .

$49 t^{2} + 50 t - 3000 = 0$

Step 5

Use the quadratic formula to find the solutions.

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

Step 6

Substitute the values $a = 49$ , $b = 50$ , and $c = - 3000$ into the quadratic formula and solve for $t$ .

$\frac{- 50 \pm \sqrt{50^{2} - 4 \cdot (49 \cdot - 3000)}}{2 \cdot 49}$

Step 7

Simplify.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

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

$t = \frac{- 50 \pm \sqrt{2500 - 4 \cdot 49 \cdot - 3000}}{2 \cdot 49}$

Step 7.1.2

Multiply $- 4 \cdot 49 \cdot - 3000$ .

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Step 7.1.2.1

Multiply $- 4$ by $49$ .

$t = \frac{- 50 \pm \sqrt{2500 - 196 \cdot - 3000}}{2 \cdot 49}$

Step 7.1.2.2

Multiply $- 196$ by $- 3000$ .

$t = \frac{- 50 \pm \sqrt{2500 + 588000}}{2 \cdot 49}$

Step 7.1.3

Add $2500$ and $588000$ .

$t = \frac{- 50 \pm \sqrt{590500}}{2 \cdot 49}$

Step 7.1.4

Rewrite $590500$ as $10^{2} \cdot 5905$ .

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Step 7.1.4.1

Factor $100$ out of $590500$ .

$t = \frac{- 50 \pm \sqrt{100 (5905)}}{2 \cdot 49}$

Step 7.1.4.2

Rewrite $100$ as $10^{2}$ .

$t = \frac{- 50 \pm \sqrt{10^{2} \cdot 5905}}{2 \cdot 49}$

Step 7.1.5

Pull terms out from under the radical.

$t = \frac{- 50 \pm 10 \sqrt{5905}}{2 \cdot 49}$

Step 7.2

Multiply $2$ by $49$ .

$t = \frac{- 50 \pm 10 \sqrt{5905}}{98}$

Step 7.3

Simplify $\frac{- 50 \pm 10 \sqrt{5905}}{98}$ .

$t = \frac{- 25 \pm 5 \sqrt{5905}}{49}$

Step 8

The final answer is the combination of both solutions.

$t = - \frac{25 - 5 \sqrt{5905}}{49}, - \frac{25 + 5 \sqrt{5905}}{49}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{25 - 5 \sqrt{5905}}{49}, - \frac{25 + 5 \sqrt{5905}}{49}$

Decimal Form:

$t = 7.33102018 \dots, - 8.35142834 \dots$