What are the solutions to the equation completesquare 3x^2+4x+1 ?

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

Find the zeros of completesquare 3x^2+4x+1

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

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complete the square

3 x^{2} + 4 x + 1

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

Solution steps

3 x^{2} + 4 x + 1

Write

3 x^{2} + 4 x + 1

in the form:

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

Factor out

3

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

2 a = \frac{4}{3} : a = \frac{2}{3}

Add and subtract

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

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

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

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

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

Simplify

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

3 x^{2} + 4 x - 3

\frac{g ^{2}}{200} (114 + 115) = 20

- \frac{1}{4} x^{2} - 2 x - 4 = 0

4 p^{2} - 8 p - 5 = 0

2 v^{2} + 9 v + 9 = 0

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