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

The solutions to the equation completesquare x^2+1/3 x+3 are (x+1/6)^2+107/36

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

The zeros of completesquare x^2+1/3 x+3 are (x+1/6)^2+107/36

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complete the square

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

(x + \frac{1}{6})^{2} + \frac{107}{36}

Solution steps

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

Write in the standard form

a x^{2} + b x + c

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

Write

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

in the form:

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

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

Add and subtract

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

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

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

Simplify

(x + \frac{1}{6})^{2} + \frac{107}{36}

x^{2} - 41 x + 400 = 0

x, x^{2} - x y + y^{2} = 1

8 x - 1 = 4 x^{2}

x^{2} + 8 x + 35 = 0

(x + 11) (x - 11) = 23

What are the solutions to the equation completesquare x^2+1/3 x+3 ?
The solutions to the equation completesquare x^2+1/3 x+3 are (x+1/6)^2+107/36
Find the zeros of completesquare x^2+1/3 x+3
The zeros of completesquare x^2+1/3 x+3 are (x+1/6)^2+107/36