What are the solutions to the equation completesquare x^2+4/9 x ?

The solutions to the equation completesquare x^2+4/9 x are (x+2/9)^2-4/81

Find the zeros of completesquare x^2+4/9 x

The zeros of completesquare x^2+4/9 x are (x+2/9)^2-4/81

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complete the square

x^{2} + \frac{4}{9} x

(x + \frac{2}{9})^{2} - \frac{4}{81}

Solution steps

x^{2} + \frac{4}{9} x

Write in the standard form

a x^{2} + b x + c

x^{2} + \frac{4 x}{9}

Write

x^{2} + \frac{4 x}{9}

in the form:

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

2 a = \frac{4}{9} : a = \frac{2}{9}

Add and subtract

(\frac{2}{9})^{2}

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

x^{2} + 2 a x + a^{2} = (x + a)^{2}

x^{2} + \frac{4}{9} x + (\frac{2}{9})^{2} = (x + \frac{2}{9})^{2}

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

Simplify

(x + \frac{2}{9})^{2} - \frac{4}{81}

x (2 x + 1) = 3

1156 = x^{2}

2 x^{2} + 6 x = 56

2 x^{2} + 19 x + 24 = 0

(2 x - 8) (x + 4) = 0

What are the solutions to the equation completesquare x^2+4/9 x ?
The solutions to the equation completesquare x^2+4/9 x are (x+2/9)^2-4/81
Find the zeros of completesquare x^2+4/9 x
The zeros of completesquare x^2+4/9 x are (x+2/9)^2-4/81