Solve Using the Quadratic Formula t^2-16=0

$t^{2} - 16 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 1$ , $b = 0$ , and $c = - 16$ into the quadratic formula and solve for $t$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 16)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$t = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 16}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 16$ .

Multiply $- 4$ by $1$ .

$t = \frac{0 \pm \sqrt{0 - 4 \cdot - 16}}{2 \cdot 1}$

Multiply $- 4$ by $- 16$ .

$t = \frac{0 \pm \sqrt{0 + 64}}{2 \cdot 1}$

Add $0$ and $64$ .

$t = \frac{0 \pm \sqrt{64}}{2 \cdot 1}$

Rewrite $64$ as $8^{2}$ .

$t = \frac{0 \pm \sqrt{8^{2}}}{2 \cdot 1}$

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

$t = \frac{0 \pm 8}{2 \cdot 1}$

Multiply $2$ by $1$ .

$t = \frac{0 \pm 8}{2}$

Simplify $\frac{0 \pm 8}{2}$ .

$t = \pm 4$

Step 4

The final answer is the combination of both solutions.

$t = 4, - 4$