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

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

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

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

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complete the square

3 x^{2} + 2 x + 1

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

Solution steps

3 x^{2} + 2 x + 1

Write

3 x^{2} + 2 x + 1

in the form:

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

Factor out

3

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

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

Add and subtract

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

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

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

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

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

Simplify

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

10 m^{2} + 2 = 152

x^{2} - 25 x + 150 = 0

2 x^{2} + 9 x - 16 = 0

x, 1000000 x^{2} - 6200 x + 9 = 0

\frac{x}{2} (3 x - 5) = \frac{1}{2} - 3 x

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