What are the solutions to the equation completesquare 12-2x-3x^2 ?

The solutions to the equation completesquare 12-2x-3x^2 are -3(x+1/3)^2+37/3

Find the zeros of completesquare 12-2x-3x^2

The zeros of completesquare 12-2x-3x^2 are -3(x+1/3)^2+37/3

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complete the square

12 - 2 x - 3 x^{2}

- 3 (x + \frac{1}{3})^{2} + \frac{37}{3}

Solution steps

12 - 2 x - 3 x^{2}

Write in the standard form

a x^{2} + b x + c

- 3 x^{2} - 2 x + 12

Write

- 3 x^{2} - 2 x + 12

in the form:

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

Factor out

- 3

- 3 (x^{2} + \frac{2 x}{3} - 4)

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

Add and subtract

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

- 3 (x^{2} + \frac{2 x}{3} - 4 + (\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} - 4 - (\frac{1}{3})^{2})

Simplify

- 3 (x + \frac{1}{3})^{2} + \frac{37}{3}

b^{2} = 11 b

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

4 x^{2} - 13 + 3 = 0

6 x^{2} + 4 x - 12 = 0

e = \frac{1}{2} m v^{2}

What are the solutions to the equation completesquare 12-2x-3x^2 ?
The solutions to the equation completesquare 12-2x-3x^2 are -3(x+1/3)^2+37/3
Find the zeros of completesquare 12-2x-3x^2
The zeros of completesquare 12-2x-3x^2 are -3(x+1/3)^2+37/3