Solve for X X^2-8X+5=0

$X^{2} - 8 X + 5 = 0$

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 $a = 1$ , $b = - 8$ , and $c = 5$ into the quadratic formula and solve for $X$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot 5)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$X = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot 5}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 5$ .

Multiply $- 4$ by $1$ .

$X = \frac{8 \pm \sqrt{64 - 4 \cdot 5}}{2 \cdot 1}$

Multiply $- 4$ by $5$ .

$X = \frac{8 \pm \sqrt{64 - 20}}{2 \cdot 1}$

Subtract $20$ from $64$ .

$X = \frac{8 \pm \sqrt{44}}{2 \cdot 1}$

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$X = \frac{8 \pm \sqrt{4 (11)}}{2 \cdot 1}$

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

$X = \frac{8 \pm \sqrt{2^{2} \cdot 11}}{2 \cdot 1}$

Pull terms out from under the radical.

$X = \frac{8 \pm 2 \sqrt{11}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$X = \frac{8 \pm 2 \sqrt{11}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{11}}{2}$ .

$X = 4 \pm \sqrt{11}$

Step 4

The final answer is the combination of both solutions.

$X = 4 + \sqrt{11}, 4 - \sqrt{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$X = 4 + \sqrt{11}, 4 - \sqrt{11}$

Decimal Form:

$X = 7.31662479 \dots, 0.68337520 \dots$