What are the solutions to the equation completesquare x^2-2/3 x+6 ?

The solutions to the equation completesquare x^2-2/3 x+6 are (x-1/3)^2+53/9

Find the zeros of completesquare x^2-2/3 x+6

The zeros of completesquare x^2-2/3 x+6 are (x-1/3)^2+53/9

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complete the square

x^{2} - \frac{2}{3} x + 6

(x - \frac{1}{3})^{2} + \frac{53}{9}

Solution steps

x^{2} - \frac{2}{3} x + 6

Write in the standard form

a x^{2} + b x + c

x^{2} - \frac{2 x}{3} + 6

Write

x^{2} - \frac{2 x}{3} + 6

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

Simplify

(x - \frac{1}{3})^{2} + \frac{53}{9}

2 x^{2} + 11 x - 3 = 0

2 x^{2} = 1 + x^{2}

0 = x^{2} - x + 1

7500000 = - 0.5 x^{2} + 2000 x + 6000000

3 a^{2} - 10 a + 2 = 0

What are the solutions to the equation completesquare x^2-2/3 x+6 ?
The solutions to the equation completesquare x^2-2/3 x+6 are (x-1/3)^2+53/9
Find the zeros of completesquare x^2-2/3 x+6
The zeros of completesquare x^2-2/3 x+6 are (x-1/3)^2+53/9