Precalculus Examples

$50 - t^{2} = 0$

Step 1

Subtract $50$ from both sides of the equation.

$- t^{2} = - 50$

Step 2

Divide each term in $- t^{2} = - 50$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- t^{2} = - 50$ by $- 1$ .

$\frac{- t^{2}}{- 1} = \frac{- 50}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{t^{2}}{1} = \frac{- 50}{- 1}$

Step 2.2.2

Divide $t^{2}$ by $1$ .

$t^{2} = \frac{- 50}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 50$ by $- 1$ .

$t^{2} = 50$

Step 3

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

$t = \pm \sqrt{50}$

Step 4

Simplify $\pm \sqrt{50}$ .

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Step 4.1

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 4.1.1

Factor $25$ out of $50$ .

$t = \pm \sqrt{25 (2)}$

Step 4.1.2

Rewrite $25$ as $5^{2}$ .

$t = \pm \sqrt{5^{2} \cdot 2}$

Step 4.2

Pull terms out from under the radical.

$t = \pm 5 \sqrt{2}$

Step 5

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

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Step 5.1

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

$t = 5 \sqrt{2}$

Step 5.2

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

$t = - 5 \sqrt{2}$

Step 5.3

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

$t = 5 \sqrt{2}, - 5 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = 5 \sqrt{2}, - 5 \sqrt{2}$

Decimal Form:

$t = 7.07106781 \dots, - 7.07106781 \dots$