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

The solutions to the equation completesquare-3x^2+2x+1 are -3(x-1/3)^2+4/3

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

The zeros of completesquare-3x^2+2x+1 are -3(x-1/3)^2+4/3

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complete the square

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

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

Solution steps

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

Write

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

in the form:

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

Factor out

- 3

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

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

Add and subtract

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

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

Simplify

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

4.9 x^{2} - 10 x = 0

U, A = 18 X^{2} - 27 X U^{2}

q^{2} = - 5

21 = x^{2} - 4 x

\frac{1}{4} (x + 3)^{2} + 6 = 0

What are the solutions to the equation completesquare-3x^2+2x+1 ?
The solutions to the equation completesquare-3x^2+2x+1 are -3(x-1/3)^2+4/3
Find the zeros of completesquare-3x^2+2x+1
The zeros of completesquare-3x^2+2x+1 are -3(x-1/3)^2+4/3