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

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

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

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

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complete the square

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

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

Solution steps

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

Write in the standard form

a x^{2} + b x + c

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

Write

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

Simplify

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

\frac{9.81}{2} x^{2} - 90 x - 150 = 0

\frac{1}{10} x^{2} - 10 = 0

x^{(2)} - 3 x + 2 = e^{(3)}

z, x^{2} + y^{2} + (z - 1)^{2} = 1

x, y = \frac{1}{4} x^{2}

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