What are the solutions to the equation x^2+x+1/3 =0 ?

The solutions to the equation x^2+x+1/3 =0 are x=-1/2+i(sqrt(3))/6 ,x=-1/2-i(sqrt(3))/6

Find the zeros of x^2+x+1/3 =0

The zeros of x^2+x+1/3 =0 are x=-1/2+i(sqrt(3))/6 ,x=-1/2-i(sqrt(3))/6

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x^{2} + x + \frac{1}{3} = 0

x = - \frac{1}{2} + i \frac{3}{6}, x = - \frac{1}{2} - i \frac{3}{6}

Solution steps

x^{2} + x + \frac{1}{3} = 0

Multiply both sides by

3

3 x^{2} + 3 x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 3 \cdot 1}{2 \cdot 3}

Simplify

3^{2} - 4 \cdot 3 \cdot 1 : 3 i

x_{1, 2} = \frac{- 3 \pm 3 i}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 3 + 3 i}{2 \cdot 3}, x_{2} = \frac{- 3 - 3 i}{2 \cdot 3}

x = \frac{- 3 + 3 i}{2 \cdot 3} : - \frac{1}{2} + i \frac{3}{6}

x = \frac{- 3 - 3 i}{2 \cdot 3} : - \frac{1}{2} - i \frac{3}{6}

The solutions to the quadratic equation are:

x = - \frac{1}{2} + i \frac{3}{6}, x = - \frac{1}{2} - i \frac{3}{6}

- 4 x^{2} + 10 x - 4 = 0

x, x^{2} - 18 x y + y^{2} = 18

6 x^{2} + 6 x + 16 = 5 x^{2} + 2

0 = 6 x^{2} + 18

x, 13 x^{2} - 10 x y + 13 y^{2} = 72

What are the solutions to the equation x^2+x+1/3 =0 ?
The solutions to the equation x^2+x+1/3 =0 are x=-1/2+i(sqrt(3))/6 ,x=-1/2-i(sqrt(3))/6
Find the zeros of x^2+x+1/3 =0
The zeros of x^2+x+1/3 =0 are x=-1/2+i(sqrt(3))/6 ,x=-1/2-i(sqrt(3))/6