What are the solutions to the equation completesquare x^2-5/3 x ?

The solutions to the equation completesquare x^2-5/3 x are (x-5/6)^2-25/36

Find the zeros of completesquare x^2-5/3 x

The zeros of completesquare x^2-5/3 x are (x-5/6)^2-25/36

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complete the square

x^{2} - \frac{5}{3} x

(x - \frac{5}{6})^{2} - \frac{25}{36}

Solution steps

x^{2} - \frac{5}{3} x

Write in the standard form

a x^{2} + b x + c

x^{2} - \frac{5 x}{3}

Write

x^{2} - \frac{5 x}{3}

in the form:

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

2 a = - \frac{5}{3} : a = - \frac{5}{6}

Add and subtract

(- \frac{5}{6})^{2}

x^{2} - \frac{5 x}{3} + (- \frac{5}{6})^{2} - (- \frac{5}{6})^{2}

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

x^{2} - \frac{5}{3} x + (- \frac{5}{6})^{2} = (x - \frac{5}{6})^{2}

(x - \frac{5}{6})^{2} - (- \frac{5}{6})^{2}

Simplify

(x - \frac{5}{6})^{2} - \frac{25}{36}

x^{2} = 12 (x - 5)

ab c x^{2} - (a^{2} b^{2} + c^{2}) x + ab c = 0

- 22 - 3 x^{2} - 2 x = - 3

- 3 x^{2} = 12

12 x^{2} - 24 = 0

What are the solutions to the equation completesquare x^2-5/3 x ?
The solutions to the equation completesquare x^2-5/3 x are (x-5/6)^2-25/36
Find the zeros of completesquare x^2-5/3 x
The zeros of completesquare x^2-5/3 x are (x-5/6)^2-25/36