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)^2-19/3

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

The zeros of completesquare 3x^2+2x-6 are 3(x+1/3)^2-19/3

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complete the square

3 x^{2} + 2 x - 6

3 (x + \frac{1}{3})^{2} - \frac{19}{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{19}{3}

s^{2} = 25

(x + 5)^{3} - x^{3} - 1 5^{2} = 50

y^{2} - y - 3 = 0

- 5 k^{2} = - 20

0 = - x^{2} + 14 x

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)^2-19/3
Find the zeros of completesquare 3x^2+2x-6
The zeros of completesquare 3x^2+2x-6 are 3(x+1/3)^2-19/3