Solve Using the Quadratic Formula y^2-8y+1=0

$y^{2} - 8 y + 1 = 0$

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 $c = 1$ into the quadratic formula and solve for $y$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $1$ .

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

Subtract $4$ from $64$ .

$y = \frac{8 \pm \sqrt{60}}{2 \cdot 1}$

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$y = \frac{8 \pm \sqrt{4 (15)}}{2 \cdot 1}$

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

$y = \frac{8 \pm \sqrt{2^{2} \cdot 15}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{8 \pm 2 \sqrt{15}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{8 \pm 2 \sqrt{15}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{15}}{2}$ .

$y = 4 \pm \sqrt{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = 4 \pm \sqrt{15}$

Decimal Form:

$y = 7.87298334 \dots, 0.12701665 \dots$