Solve for t 3984=16t^2

$3984 = 16 t^{2}$

Step 1

Rewrite the equation as $16 t^{2} = 3984$ .

$16 t^{2} = 3984$

Step 2

Divide each term in $16 t^{2} = 3984$ by $16$ and simplify.

Divide each term in $16 t^{2} = 3984$ by $16$ .

$\frac{16 t^{2}}{16} = \frac{3984}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 t^{2}}{16} = \frac{3984}{16}$

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

$t^{2} = \frac{3984}{16}$

Simplify the right side.

Divide $3984$ by $16$ .

$t^{2} = 249$

Step 3

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

$t = \pm \sqrt{249}$

Step 4

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

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

$t = \sqrt{249}$

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

$t = - \sqrt{249}$

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

$t = \sqrt{249}, - \sqrt{249}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \sqrt{249}, - \sqrt{249}$

Decimal Form:

$t = 15.77973383 \dots, - 15.77973383 \dots$