What are the solutions to the equation completesquare x^2+(2x)/3-1/3 ?

The solutions to the equation completesquare x^2+(2x)/3-1/3 are (x+1/3)^2-4/9

Find the zeros of completesquare x^2+(2x)/3-1/3

The zeros of completesquare x^2+(2x)/3-1/3 are (x+1/3)^2-4/9

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complete the square

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

(x + \frac{1}{3})^{2} - \frac{4}{9}

Solution steps

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

Write

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

in the form:

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

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

Add and subtract

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

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}

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

Simplify

(x + \frac{1}{3})^{2} - \frac{4}{9}

2 - 2 y^{2} = 2 y^{2} - 2

x^{2} - 16 x - 80 = 0

6 z^{2} + 13 z + 6 = 0

4 u^{2} - 5 u + 1 = 0

6 x = 4 - x^{2}

What are the solutions to the equation completesquare x^2+(2x)/3-1/3 ?
The solutions to the equation completesquare x^2+(2x)/3-1/3 are (x+1/3)^2-4/9
Find the zeros of completesquare x^2+(2x)/3-1/3
The zeros of completesquare x^2+(2x)/3-1/3 are (x+1/3)^2-4/9