Solve Using the Quadratic Formula y^2-10y+20=0

$y^{2} - 10 y + 20 = 0$

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 $a = 1$ , $b = - 10$ , and $c = 20$ into the quadratic formula and solve for $y$ .

$\frac{10 \pm \sqrt{{(- 10)}^{2} - 4 \cdot (1 \cdot 20)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 10$ to the power of $2$ .

$y = \frac{10 \pm \sqrt{100 - 4 \cdot 1 \cdot 20}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 20$ .

Multiply $- 4$ by $1$ .

$y = \frac{10 \pm \sqrt{100 - 4 \cdot 20}}{2 \cdot 1}$

Multiply $- 4$ by $20$ .

$y = \frac{10 \pm \sqrt{100 - 80}}{2 \cdot 1}$

Subtract $80$ from $100$ .

$y = \frac{10 \pm \sqrt{20}}{2 \cdot 1}$

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

Factor $4$ out of $20$ .

$y = \frac{10 \pm \sqrt{4 (5)}}{2 \cdot 1}$

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

$y = \frac{10 \pm \sqrt{2^{2} \cdot 5}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{10 \pm 2 \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{10 \pm 2 \sqrt{5}}{2}$

Simplify $\frac{10 \pm 2 \sqrt{5}}{2}$ .

$y = 5 \pm \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = 5 \pm \sqrt{5}$

Decimal Form:

$y = 7.23606797 \dots, 2.76393202 \dots$