Basic Math Examples

$0 = 1.4 t^{2} - 5 t + 2.8$

Step 1

Rewrite the equation as $1.4 t^{2} - 5 t + 2.8 = 0$ .

$1.4 t^{2} - 5 t + 2.8 = 0$

Step 2

Factor $0.2$ out of $1.4 t^{2} - 5 t + 2.8$ .

Tap for more steps...

Step 2.1

Factor $0.2$ out of $1.4 t^{2}$ .

$0.2 (7 t^{2}) - 5 t + 2.8 = 0$

Step 2.2

Factor $0.2$ out of $- 5 t$ .

$0.2 (7 t^{2}) + 0.2 (- 25 t) + 2.8 = 0$

Step 2.3

Factor $0.2$ out of $2.8$ .

$0.2 (7 t^{2}) + 0.2 (- 25 t) + 0.2 (14) = 0$

Step 2.4

Factor $0.2$ out of $0.2 (7 t^{2}) + 0.2 (- 25 t)$ .

$0.2 (7 t^{2} - 25 t) + 0.2 (14) = 0$

Step 2.5

Factor $0.2$ out of $0.2 (7 t^{2} - 25 t) + 0.2 (14)$ .

$0.2 (7 t^{2} - 25 t + 14) = 0$

Step 3

Divide each term in $0.2 (7 t^{2} - 25 t + 14) = 0$ by $0.2$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $0.2 (7 t^{2} - 25 t + 14) = 0$ by $0.2$ .

$\frac{0.2 (7 t^{2} - 25 t + 14)}{0.2} = \frac{0}{0.2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $0.2$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{0.2 (7 t^{2} - 25 t + 14)}{0.2} = \frac{0}{0.2}$

Step 3.2.1.2

Divide $7 t^{2} - 25 t + 14$ by $1$ .

$7 t^{2} - 25 t + 14 = \frac{0}{0.2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $0$ by $0.2$ .

$7 t^{2} - 25 t + 14 = 0$

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = 7$ , $b = - 25$ , and $c = 14$ into the quadratic formula and solve for $t$ .

$\frac{25 \pm \sqrt{{(- 25)}^{2} - 4 \cdot (7 \cdot 14)}}{2 \cdot 7}$

Step 6

Simplify.

Tap for more steps...

Step 6.1

Simplify the numerator.

Tap for more steps...

Step 6.1.1

Raise $- 25$ to the power of $2$ .

$t = \frac{25 \pm \sqrt{625 - 4 \cdot 7 \cdot 14}}{2 \cdot 7}$

Step 6.1.2

Multiply $- 4 \cdot 7 \cdot 14$ .

Tap for more steps...

Step 6.1.2.1

Multiply $- 4$ by $7$ .

$t = \frac{25 \pm \sqrt{625 - 28 \cdot 14}}{2 \cdot 7}$

Step 6.1.2.2

Multiply $- 28$ by $14$ .

$t = \frac{25 \pm \sqrt{625 - 392}}{2 \cdot 7}$

Step 6.1.3

Subtract $392$ from $625$ .

$t = \frac{25 \pm \sqrt{233}}{2 \cdot 7}$

Step 6.2

Multiply $2$ by $7$ .

$t = \frac{25 \pm \sqrt{233}}{14}$

Step 7

The final answer is the combination of both solutions.

$t = \frac{25 + \sqrt{233}}{14}, \frac{25 - \sqrt{233}}{14}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$t = \frac{25 + \sqrt{233}}{14}, \frac{25 - \sqrt{233}}{14}$

Decimal Form:

$t = 2.87602410 \dots, 0.69540446 \dots$