What are the solutions to the equation completesquare y^2+y+1 ?

The solutions to the equation completesquare y^2+y+1 are (y+1/2)^2+3/4

Find the zeros of completesquare y^2+y+1

The zeros of completesquare y^2+y+1 are (y+1/2)^2+3/4

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complete the square

y^{2} + y + 1

(y + \frac{1}{2})^{2} + \frac{3}{4}

Solution steps

y^{2} + y + 1

Write

y^{2} + y + 1

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

Simplify

(y + \frac{1}{2})^{2} + \frac{3}{4}

x, x^{2} - 8 x = - x

x, f (x - 1) = x^{2} + 1

5 x^{2} + 12 x - 2 = 0

y^{2} - 6 y + 9 = - 25

3 x^{2} - 2 x + 1

What are the solutions to the equation completesquare y^2+y+1 ?
The solutions to the equation completesquare y^2+y+1 are (y+1/2)^2+3/4
Find the zeros of completesquare y^2+y+1
The zeros of completesquare y^2+y+1 are (y+1/2)^2+3/4