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

The solutions to the equation completesquare 3x^2-2x+6 are 3(x-1/3)^2+17/3

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

The zeros of completesquare 3x^2-2x+6 are 3(x-1/3)^2+17/3

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complete the square

3 x^{2} - 2 x + 6

3 (x - \frac{1}{3})^{2} + \frac{17}{3}

Solution steps

3 x^{2} - 2 x + 6

Write

3 x^{2} - 2 x + 6

in the form:

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

Factor out

3

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

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

Add and subtract

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

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

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

Simplify

3 (x - \frac{1}{3})^{2} + \frac{17}{3}

3 x^{2} - 2 x + 5

6 x^{2} - 17 x - 14 = 0

m^{2} - 12 m + 26 = 0

3 t^{2} - 8 t + 5 = 0

2 x^{2} - 8 x = 14

What are the solutions to the equation completesquare 3x^2-2x+6 ?
The solutions to the equation completesquare 3x^2-2x+6 are 3(x-1/3)^2+17/3
Find the zeros of completesquare 3x^2-2x+6
The zeros of completesquare 3x^2-2x+6 are 3(x-1/3)^2+17/3