Solve y^2+y/2-1/16

$${ y }^{ 2 } + \frac{ y }{ 2 } - \frac{ 1 }{ 16 }$$

Evaluate

$$y^{2}+\frac{y}{2}-\frac{1}{16}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 16 is 16. Multiply \frac{y}{2} times \frac{8}{8}.

$$y^{2}+\frac{8y}{16}-\frac{1}{16}$$

Since \frac{8y}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$y^{2}+\frac{8y-1}{16}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y^{2} times \frac{16}{16}.

$$\frac{16y^{2}}{16}+\frac{8y-1}{16}$$

Since \frac{16y^{2}}{16} and \frac{8y-1}{16} have the same denominator, add them by adding their numerators.

$$\frac{16y^{2}+8y-1}{16}$$

Divide each term of 16y^{2}+8y-1 by 16 to get \frac{1}{2}y+y^{2}-\frac{1}{16}.

$$\frac{1}{2}y+y^{2}-\frac{1}{16}$$

Factor

$$\left(y-\frac{-\sqrt{2}-1}{4}\right)\left(y-\frac{\sqrt{2}-1}{4}\right)$$