What are the solutions to the equation completesquare-3x^2+6x-1 ?

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

Find the zeros of completesquare-3x^2+6x-1

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

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complete the square

- 3 x^{2} + 6 x - 1

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

Solution steps

- 3 x^{2} + 6 x - 1

Write

- 3 x^{2} + 6 x - 1

in the form:

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

Factor out

- 3

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

2 a = - 2 : a = - 1

Add and subtract

(- 1)^{2}

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

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

x^{2} - 2 x + (- 1)^{2} = (x - 1)^{2}

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

Simplify

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

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

x, x \cdot (x - y) + y \cdot (y - z) + z \cdot (z - x) = 1

n^{2} - 12 n = - 17

6 x^{2} + 6 = - 13 x

2 x^{2} + 7 x - 30 = 64 (x + 6)

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