Solve Using the Square Root Property 784=16t^2

$784 = 16 t^{2}$

Step 1

Rewrite the equation as $16 t^{2} = 784$ .

$16 t^{2} = 784$

Step 2

Divide each term in $16 t^{2} = 784$ by $16$ and simplify.

Divide each term in $16 t^{2} = 784$ by $16$ .

$\frac{16 t^{2}}{16} = \frac{784}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 t^{2}}{16} = \frac{784}{16}$

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

$t^{2} = \frac{784}{16}$

Simplify the right side.

Divide $784$ by $16$ .

$t^{2} = 49$

Step 3

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

$t = \pm \sqrt{49}$

Step 4

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$t = \pm \sqrt{7^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$t = \pm 7$

Step 5

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.

$t = 7$

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

$t = - 7$

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

$t = 7, - 7$