Basic Math Examples

$\frac{t^{2}}{20} + 8 = 15$

Step 1

Move all terms not containing $t$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $8$ from both sides of the equation.

$\frac{t^{2}}{20} = 15 - 8$

Step 1.2

Subtract $8$ from $15$ .

$\frac{t^{2}}{20} = 7$

Step 2

Multiply both sides of the equation by $20$ .

$20 \frac{t^{2}}{20} = 20 \cdot 7$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $20$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$20 \frac{t^{2}}{20} = 20 \cdot 7$

Step 3.1.1.2

Rewrite the expression.

$t^{2} = 20 \cdot 7$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $20$ by $7$ .

$t^{2} = 140$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$t = \pm \sqrt{140}$

Step 5

Simplify $\pm \sqrt{140}$ .

Tap for more steps...

Step 5.1

Rewrite $140$ as $2^{2} \cdot 35$ .

Tap for more steps...

Step 5.1.1

Factor $4$ out of $140$ .

$t = \pm \sqrt{4 (35)}$

Step 5.1.2

Rewrite $4$ as $2^{2}$ .

$t = \pm \sqrt{2^{2} \cdot 35}$

Step 5.2

Pull terms out from under the radical.

$t = \pm 2 \sqrt{35}$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

Step 6.1

First, use the positive value of the $\pm$ to find the first solution.

$t = 2 \sqrt{35}$

Step 6.2

Next, use the negative value of the $\pm$ to find the second solution.

$t = - 2 \sqrt{35}$

Step 6.3

The complete solution is the result of both the positive and negative portions of the solution.

$t = 2 \sqrt{35}, - 2 \sqrt{35}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$t = 2 \sqrt{35}, - 2 \sqrt{35}$

Decimal Form:

$t = 11.83215956 \dots, - 11.83215956 \dots$