Solve Using the Quadratic Formula y(y+1)-4=0

$y (y + 1) - 4 = 0$

Step 1

Simplify the left side.

Simplify each term.

Apply the distributive property.

$y \cdot y + y \cdot 1 - 4 = 0$

Multiply $y$ by $y$ .

$y^{2} + y \cdot 1 - 4 = 0$

Multiply $y$ by $1$ .

$y^{2} + y - 4 = 0$

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 $a = 1$ , $b = 1$ , and $c = - 4$ into the quadratic formula and solve for $y$ .

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

Step 4

Simplify.

Simplify the numerator.

One to any power is one.

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

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

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $- 4$ .

$y = \frac{- 1 \pm \sqrt{1 + 16}}{2 \cdot 1}$

Add $1$ and $16$ .

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

Multiply $2$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 1.56155281 \dots, - 2.56155281 \dots$