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

The solutions to the equation completesquare 3x^2+2x+2 are 3(x+1/3)^2+5/3

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

The zeros of completesquare 3x^2+2x+2 are 3(x+1/3)^2+5/3

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complete the square

3 x^{2} + 2 x + 2

3 (x + \frac{1}{3})^{2} + \frac{5}{3}

Solution steps

3 x^{2} + 2 x + 2

Write

3 x^{2} + 2 x + 2

in the form:

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

Factor out

3

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

Simplify

3 (x + \frac{1}{3})^{2} + \frac{5}{3}

25 (5 x - 1)^{2} - 40 = - 4

y, x^{2} = 4 y^{2}

6 x^{2} - 30 x = 0

x^{2} = - 32 + 12 x

x^{2} - 7 = 6 x

What are the solutions to the equation completesquare 3x^2+2x+2 ?
The solutions to the equation completesquare 3x^2+2x+2 are 3(x+1/3)^2+5/3
Find the zeros of completesquare 3x^2+2x+2
The zeros of completesquare 3x^2+2x+2 are 3(x+1/3)^2+5/3