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

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

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

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

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complete the square

s^{2} + s + 1

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

Solution steps

s^{2} + s + 1

Write

s^{2} + s + 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}

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

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

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

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

Simplify

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

5 x^{2} - 36 x + 36 = 0

(x + 3) (x - 6) = 0

x^{2} + 3 x - 5

- 2 x^{2} + 20 x - 68 = 0

x, x^{2} - 6 x y - 7 y^{2} + 10 x + 2 y + 17 = 0

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