Pre-Algebra Examples

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

Step 1

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

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

Step 2

Subtract $300$ from both sides of the equation.

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

Factor $0.1$ out of $2 t$ .

$0.1 (49 t^{2}) + 0.1 (20 t) - 300 = 0$

Step 3.3

Factor $0.1$ out of $- 300$ .

$0.1 (49 t^{2}) + 0.1 (20 t) + 0.1 (- 3000) = 0$

Step 3.4

Factor $0.1$ out of $0.1 (49 t^{2}) + 0.1 (20 t)$ .

$0.1 (49 t^{2} + 20 t) + 0.1 (- 3000) = 0$

Step 3.5

Factor $0.1$ out of $0.1 (49 t^{2} + 20 t) + 0.1 (- 3000)$ .

$0.1 (49 t^{2} + 20 t - 3000) = 0$

Step 4

Divide each term in $0.1 (49 t^{2} + 20 t - 3000) = 0$ by $0.1$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $0.1 (49 t^{2} + 20 t - 3000) = 0$ by $0.1$ .

$\frac{0.1 (49 t^{2} + 20 t - 3000)}{0.1} = \frac{0}{0.1}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $0.1$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{0.1 (49 t^{2} + 20 t - 3000)}{0.1} = \frac{0}{0.1}$

Step 4.2.1.2

Divide $49 t^{2} + 20 t - 3000$ by $1$ .

$49 t^{2} + 20 t - 3000 = \frac{0}{0.1}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $0$ by $0.1$ .

$49 t^{2} + 20 t - 3000 = 0$

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 $a = 49$ , $b = 20$ , and $c = - 3000$ into the quadratic formula and solve for $t$ .

$\frac{- 20 \pm \sqrt{20^{2} - 4 \cdot (49 \cdot - 3000)}}{2 \cdot 49}$

Step 7

Simplify.

Tap for more steps...

Step 7.1

Simplify the numerator.

Tap for more steps...

Step 7.1.1

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

$t = \frac{- 20 \pm \sqrt{400 - 4 \cdot 49 \cdot - 3000}}{2 \cdot 49}$

Step 7.1.2

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

Tap for more steps...

Step 7.1.2.1

Multiply $- 4$ by $49$ .

$t = \frac{- 20 \pm \sqrt{400 - 196 \cdot - 3000}}{2 \cdot 49}$

Step 7.1.2.2

Multiply $- 196$ by $- 3000$ .

$t = \frac{- 20 \pm \sqrt{400 + 588000}}{2 \cdot 49}$

Step 7.1.3

Add $400$ and $588000$ .

$t = \frac{- 20 \pm \sqrt{588400}}{2 \cdot 49}$

Step 7.1.4

Rewrite $588400$ as $20^{2} \cdot 1471$ .

Tap for more steps...

Step 7.1.4.1

Factor $400$ out of $588400$ .

$t = \frac{- 20 \pm \sqrt{400 (1471)}}{2 \cdot 49}$

Step 7.1.4.2

Rewrite $400$ as $20^{2}$ .

$t = \frac{- 20 \pm \sqrt{20^{2} \cdot 1471}}{2 \cdot 49}$

Step 7.1.5

Pull terms out from under the radical.

$t = \frac{- 20 \pm 20 \sqrt{1471}}{2 \cdot 49}$

Step 7.2

Multiply $2$ by $49$ .

$t = \frac{- 20 \pm 20 \sqrt{1471}}{98}$

Step 7.3

Simplify $\frac{- 20 \pm 20 \sqrt{1471}}{98}$ .

$t = \frac{- 10 \pm 10 \sqrt{1471}}{49}$

Step 8

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Tap for more steps...

Step 8.1

Simplify the numerator.

Tap for more steps...

Step 8.1.1

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

$t = \frac{- 20 \pm \sqrt{400 - 4 \cdot 49 \cdot - 3000}}{2 \cdot 49}$

Step 8.1.2

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

Tap for more steps...

Step 8.1.2.1

Multiply $- 4$ by $49$ .

$t = \frac{- 20 \pm \sqrt{400 - 196 \cdot - 3000}}{2 \cdot 49}$

Step 8.1.2.2

Multiply $- 196$ by $- 3000$ .

$t = \frac{- 20 \pm \sqrt{400 + 588000}}{2 \cdot 49}$

Step 8.1.3

Add $400$ and $588000$ .

$t = \frac{- 20 \pm \sqrt{588400}}{2 \cdot 49}$

Step 8.1.4

Rewrite $588400$ as $20^{2} \cdot 1471$ .

Tap for more steps...

Step 8.1.4.1

Factor $400$ out of $588400$ .

$t = \frac{- 20 \pm \sqrt{400 (1471)}}{2 \cdot 49}$

Step 8.1.4.2

Rewrite $400$ as $20^{2}$ .

$t = \frac{- 20 \pm \sqrt{20^{2} \cdot 1471}}{2 \cdot 49}$

Step 8.1.5

Pull terms out from under the radical.

$t = \frac{- 20 \pm 20 \sqrt{1471}}{2 \cdot 49}$

Step 8.2

Multiply $2$ by $49$ .

$t = \frac{- 20 \pm 20 \sqrt{1471}}{98}$

Step 8.3

Simplify $\frac{- 20 \pm 20 \sqrt{1471}}{98}$ .

$t = \frac{- 10 \pm 10 \sqrt{1471}}{49}$

Step 8.4

Change the $\pm$ to $+$ .

$t = \frac{- 10 + 10 \sqrt{1471}}{49}$

Step 8.5

Rewrite $- 10$ as $- 1 (10)$ .

$t = \frac{- 1 \cdot 10 + 10 \sqrt{1471}}{49}$

Step 8.6

Factor $- 1$ out of $10 \sqrt{1471}$ .

$t = \frac{- 1 \cdot 10 - (- 10 \sqrt{1471})}{49}$

Step 8.7

Factor $- 1$ out of $- 1 (10) - (- 10 \sqrt{1471})$ .

$t = \frac{- 1 (10 - 10 \sqrt{1471})}{49}$

Step 8.8

Move the negative in front of the fraction.

$t = - \frac{10 - 10 \sqrt{1471}}{49}$

Step 9

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Tap for more steps...

Step 9.1

Simplify the numerator.

Tap for more steps...

Step 9.1.1

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

$t = \frac{- 20 \pm \sqrt{400 - 4 \cdot 49 \cdot - 3000}}{2 \cdot 49}$

Step 9.1.2

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

Tap for more steps...

Step 9.1.2.1

Multiply $- 4$ by $49$ .

$t = \frac{- 20 \pm \sqrt{400 - 196 \cdot - 3000}}{2 \cdot 49}$

Step 9.1.2.2

Multiply $- 196$ by $- 3000$ .

$t = \frac{- 20 \pm \sqrt{400 + 588000}}{2 \cdot 49}$

Step 9.1.3

Add $400$ and $588000$ .

$t = \frac{- 20 \pm \sqrt{588400}}{2 \cdot 49}$

Step 9.1.4

Rewrite $588400$ as $20^{2} \cdot 1471$ .

Tap for more steps...

Step 9.1.4.1

Factor $400$ out of $588400$ .

$t = \frac{- 20 \pm \sqrt{400 (1471)}}{2 \cdot 49}$

Step 9.1.4.2

Rewrite $400$ as $20^{2}$ .

$t = \frac{- 20 \pm \sqrt{20^{2} \cdot 1471}}{2 \cdot 49}$

Step 9.1.5

Pull terms out from under the radical.

$t = \frac{- 20 \pm 20 \sqrt{1471}}{2 \cdot 49}$

Step 9.2

Multiply $2$ by $49$ .

$t = \frac{- 20 \pm 20 \sqrt{1471}}{98}$

Step 9.3

Simplify $\frac{- 20 \pm 20 \sqrt{1471}}{98}$ .

$t = \frac{- 10 \pm 10 \sqrt{1471}}{49}$

Step 9.4

Change the $\pm$ to $-$ .

$t = \frac{- 10 - 10 \sqrt{1471}}{49}$

Step 9.5

Rewrite $- 10$ as $- 1 (10)$ .

$t = \frac{- 1 \cdot 10 - 10 \sqrt{1471}}{49}$

Step 9.6

Factor $- 1$ out of $- 10 \sqrt{1471}$ .

$t = \frac{- 1 \cdot 10 - (10 \sqrt{1471})}{49}$

Step 9.7

Factor $- 1$ out of $- 1 (10) - (10 \sqrt{1471})$ .

$t = \frac{- 1 (10 + 10 \sqrt{1471})}{49}$

Step 9.8

Move the negative in front of the fraction.

$t = - \frac{10 + 10 \sqrt{1471}}{49}$

Step 10

The final answer is the combination of both solutions.

$t = - \frac{10 - 10 \sqrt{1471}}{49}, - \frac{10 + 10 \sqrt{1471}}{49}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{10 - 10 \sqrt{1471}}{49}, - \frac{10 + 10 \sqrt{1471}}{49}$

Decimal Form:

$t = 7.62318731 \dots, - 8.03135057 \dots$