What are the solutions to the equation completesquare 3x^2+x+1 ?

The solutions to the equation completesquare 3x^2+x+1 are 3(x+1/6)^2+11/12

Find the zeros of completesquare 3x^2+x+1

The zeros of completesquare 3x^2+x+1 are 3(x+1/6)^2+11/12

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complete the square

3 x^{2} + x + 1

3 (x + \frac{1}{6})^{2} + \frac{11}{12}

Solution steps

3 x^{2} + x + 1

Write

3 x^{2} + x + 1

in the form:

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

Factor out

3

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

2 a = \frac{1}{3} : a = \frac{1}{6}

Add and subtract

(\frac{1}{6})^{2}

3 (x^{2} + \frac{x}{3} + \frac{1}{3} + (\frac{1}{6})^{2} - (\frac{1}{6})^{2})

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

x^{2} + \frac{1}{3} x + (\frac{1}{6})^{2} = (x + \frac{1}{6})^{2}

3 ((x + \frac{1}{6})^{2} + \frac{1}{3} - (\frac{1}{6})^{2})

Simplify

3 (x + \frac{1}{6})^{2} + \frac{11}{12}

3 x^{2} + x - 2

- 7 x^{2} - 2 x = 1

x^{2} + \frac{x}{20} + \frac{1}{1250} = 0

13 = \frac{5 x ^{2}}{2 ( 32.2 )} - 20 + 4 (0.1 x)^{2}

What are the solutions to the equation completesquare 3x^2+x+1 ?
The solutions to the equation completesquare 3x^2+x+1 are 3(x+1/6)^2+11/12
Find the zeros of completesquare 3x^2+x+1
The zeros of completesquare 3x^2+x+1 are 3(x+1/6)^2+11/12