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

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

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

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

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complete the square

x^{2} + x + 1

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

Solution steps

x^{2} + x + 1

Write

x^{2} + x + 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}

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

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

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

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

Simplify

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

v, E = \frac{1}{2} m v^{2}

3 x^{2} + 2 x - 1

5 t^{2} - 20 t + 20 = 0

x^{2} + b x + c = 0

3 x^{2} + 5 = 5 x^{2} - 8 x

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