Solve Using the Quadratic Formula y^2-12y=-19

$y^{2} - 12 y = - 19$

Step 1

Add $19$ to both sides of the equation.

$y^{2} - 12 y + 19 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = - 12$ , and $c = 19$ into the quadratic formula and solve for $y$ .

$\frac{12 \pm \sqrt{{(- 12)}^{2} - 4 \cdot (1 \cdot 19)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 12$ to the power of $2$ .

$y = \frac{12 \pm \sqrt{144 - 4 \cdot 1 \cdot 19}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 19$ .

Multiply $- 4$ by $1$ .

$y = \frac{12 \pm \sqrt{144 - 4 \cdot 19}}{2 \cdot 1}$

Multiply $- 4$ by $19$ .

$y = \frac{12 \pm \sqrt{144 - 76}}{2 \cdot 1}$

Subtract $76$ from $144$ .

$y = \frac{12 \pm \sqrt{68}}{2 \cdot 1}$

Rewrite $68$ as $2^{2} \cdot 17$ .

Factor $4$ out of $68$ .

$y = \frac{12 \pm \sqrt{4 (17)}}{2 \cdot 1}$

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

$y = \frac{12 \pm \sqrt{2^{2} \cdot 17}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{12 \pm 2 \sqrt{17}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{12 \pm 2 \sqrt{17}}{2}$

Simplify $\frac{12 \pm 2 \sqrt{17}}{2}$ .

$y = 6 \pm \sqrt{17}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = 6 \pm \sqrt{17}$

Decimal Form:

$y = 10.12310562 \dots, 1.87689437 \dots$