Solve Using the Quadratic Formula X^2-2X-4=0

$X^{2} - 2 X - 4 = 0$

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 $a = 1$ , $b = - 2$ , and $c = - 4$ into the quadratic formula and solve for $X$ .

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

Step 3

Simplify.

Simplify the numerator.

Raise $- 2$ to the power of $2$ .

$X = \frac{2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 4}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$X = \frac{2 \pm \sqrt{4 - 4 \cdot - 4}}{2 \cdot 1}$

Multiply $- 4$ by $- 4$ .

$X = \frac{2 \pm \sqrt{4 + 16}}{2 \cdot 1}$

Add $4$ and $16$ .

$X = \frac{2 \pm \sqrt{20}}{2 \cdot 1}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$X = \frac{2 \pm \sqrt{4 (5)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$X = \frac{2 \pm \sqrt{2^{2} \cdot 5}}{2 \cdot 1}$

Pull terms out from under the radical.

$X = \frac{2 \pm 2 \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$X = \frac{2 \pm 2 \sqrt{5}}{2}$

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

$X = 1 \pm \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$X = 1 \pm \sqrt{5}$

Decimal Form:

$X = 3.23606797 \dots, - 1.23606797 \dots$