Solve Using the Quadratic Formula t^2-405=0

$t^{2} - 405 = 0$

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 $c = - 405$ into the quadratic formula and solve for $t$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 405)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$t = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 405}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 405$ .

Multiply $- 4$ by $1$ .

$t = \frac{0 \pm \sqrt{0 - 4 \cdot - 405}}{2 \cdot 1}$

Multiply $- 4$ by $- 405$ .

$t = \frac{0 \pm \sqrt{0 + 1620}}{2 \cdot 1}$

Add $0$ and $1620$ .

$t = \frac{0 \pm \sqrt{1620}}{2 \cdot 1}$

Rewrite $1620$ as $18^{2} \cdot 5$ .

Factor $324$ out of $1620$ .

$t = \frac{0 \pm \sqrt{324 (5)}}{2 \cdot 1}$

Rewrite $324$ as $18^{2}$ .

$t = \frac{0 \pm \sqrt{18^{2} \cdot 5}}{2 \cdot 1}$

Pull terms out from under the radical.

$t = \frac{0 \pm 18 \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$t = \frac{0 \pm 18 \sqrt{5}}{2}$

Simplify $\frac{0 \pm 18 \sqrt{5}}{2}$ .

$t = \pm 9 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = \pm 9 \sqrt{5}$

Decimal Form:

$t = 20.12461179 \dots, - 20.12461179 \dots$