Solve Using the Quadratic Formula y^2-8y+7=0

$y^{2} - 8 y + 7 = 0$

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 $c = 7$ into the quadratic formula and solve for $y$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot 7)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$y = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot 7}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 7$ .

Multiply $- 4$ by $1$ .

$y = \frac{8 \pm \sqrt{64 - 4 \cdot 7}}{2 \cdot 1}$

Multiply $- 4$ by $7$ .

$y = \frac{8 \pm \sqrt{64 - 28}}{2 \cdot 1}$

Subtract $28$ from $64$ .

$y = \frac{8 \pm \sqrt{36}}{2 \cdot 1}$

Rewrite $36$ as $6^{2}$ .

$y = \frac{8 \pm \sqrt{6^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$y = \frac{8 \pm 6}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{8 \pm 6}{2}$

Simplify $\frac{8 \pm 6}{2}$ .

$y = 4 \pm 3$

Step 4

The final answer is the combination of both solutions.

$y = 7, 1$