Solve Using the Quadratic Formula t^2-75=0

$t^{2} - 75 = 0$

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 $c = - 75$ into the quadratic formula and solve for $t$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 75)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$t = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 75}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 75$ .

Multiply $- 4$ by $1$ .

$t = \frac{0 \pm \sqrt{0 - 4 \cdot - 75}}{2 \cdot 1}$

Multiply $- 4$ by $- 75$ .

$t = \frac{0 \pm \sqrt{0 + 300}}{2 \cdot 1}$

Add $0$ and $300$ .

$t = \frac{0 \pm \sqrt{300}}{2 \cdot 1}$

Rewrite $300$ as $10^{2} \cdot 3$ .

Factor $100$ out of $300$ .

$t = \frac{0 \pm \sqrt{100 (3)}}{2 \cdot 1}$

Rewrite $100$ as $10^{2}$ .

$t = \frac{0 \pm \sqrt{10^{2} \cdot 3}}{2 \cdot 1}$

Pull terms out from under the radical.

$t = \frac{0 \pm 10 \sqrt{3}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$t = \frac{0 \pm 10 \sqrt{3}}{2}$

Simplify $\frac{0 \pm 10 \sqrt{3}}{2}$ .

$t = \pm 5 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = \pm 5 \sqrt{3}$

Decimal Form:

$t = 8.66025403 \dots, - 8.66025403 \dots$