What are the solutions to the equation completesquare y^2+y ?

The solutions to the equation completesquare y^2+y are (y+1/2)^2-1/4

Find the zeros of completesquare y^2+y

The zeros of completesquare y^2+y are (y+1/2)^2-1/4

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complete the square

y^{2} + y

(y + \frac{1}{2})^{2} - \frac{1}{4}

Solution steps

y^{2} + y

Write

y^{2} + y

in the form:

x^{2} + 2 a x + a^{2}

2 a = 1 : a = \frac{1}{2}

Add and subtract

(\frac{1}{2})^{2}

y^{2} + y + (\frac{1}{2})^{2} - (\frac{1}{2})^{2}

x^{2} + 2 a x + a^{2} = (x + a)^{2}

y^{2} + 1 y + (\frac{1}{2})^{2} = (y + \frac{1}{2})^{2}

(y + \frac{1}{2})^{2} - (\frac{1}{2})^{2}

Simplify

(y + \frac{1}{2})^{2} - \frac{1}{4}

x, x^{2} - 4 x = 0

x^{2} + 15 x - 100 = 0

- x^{2} + 500 x - 62.5 = 0

9 x^{2} - 12 x + 4 = 0

x^{2} + 6 x + 17 = 0

What are the solutions to the equation completesquare y^2+y ?
The solutions to the equation completesquare y^2+y are (y+1/2)^2-1/4
Find the zeros of completesquare y^2+y
The zeros of completesquare y^2+y are (y+1/2)^2-1/4