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

The solutions to the equation completesquare 3x^2+x-2 are 3(x+1/6)^2-25/12

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

The zeros of completesquare 3x^2+x-2 are 3(x+1/6)^2-25/12

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complete the square

3 x^{2} + x - 2

3 (x + \frac{1}{6})^{2} - \frac{25}{12}

Solution steps

3 x^{2} + x - 2

Write

3 x^{2} + x - 2

in the form:

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

Factor out

3

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

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

Add and subtract

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

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

Simplify

3 (x + \frac{1}{6})^{2} - \frac{25}{12}

- 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}

2 (x - 2)^{2} = 0

What are the solutions to the equation completesquare 3x^2+x-2 ?
The solutions to the equation completesquare 3x^2+x-2 are 3(x+1/6)^2-25/12
Find the zeros of completesquare 3x^2+x-2
The zeros of completesquare 3x^2+x-2 are 3(x+1/6)^2-25/12