What are the solutions to the equation 1/3 w^2+1/3 w=-1/4 ?

The solutions to the equation 1/3 w^2+1/3 w=-1/4 are w=-1/2+i(sqrt(2))/2 ,w=-1/2-i(sqrt(2))/2

Find the zeros of 1/3 w^2+1/3 w=-1/4

The zeros of 1/3 w^2+1/3 w=-1/4 are w=-1/2+i(sqrt(2))/2 ,w=-1/2-i(sqrt(2))/2

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

w = - \frac{1}{2} + i \frac{2}{2}, w = - \frac{1}{2} - i \frac{2}{2}

Solution steps

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

Find Least Common Multiplier of

3, 4 : 12

Multiply by LCM=

12

\frac{1}{3} w^{2} \cdot 12 + \frac{1}{3} w \cdot 12 = - \frac{1}{4} \cdot 12

Simplify

4 w^{2} + 4 w = - 3

Move

3

to the left side

4 w^{2} + 4 w + 3 = 0

Solve with the quadratic formula

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

Simplify

4^{2} - 4 \cdot 4 \cdot 3 : 42 i

w_{1, 2} = \frac{- 4 \pm 4 2 i}{2 \cdot 4}

Separate the solutions

w_{1} = \frac{- 4 + 4 2 i}{2 \cdot 4}, w_{2} = \frac{- 4 - 4 2 i}{2 \cdot 4}

w = \frac{- 4 + 4 2 i}{2 \cdot 4} : - \frac{1}{2} + i \frac{2}{2}

w = \frac{- 4 - 4 2 i}{2 \cdot 4} : - \frac{1}{2} - i \frac{2}{2}

The solutions to the quadratic equation are:

w = - \frac{1}{2} + i \frac{2}{2}, w = - \frac{1}{2} - i \frac{2}{2}

x^{2} - x - 6 = 9

x^{2} - 11 x - 24 = 0

x, z = x^{2} + x y + y^{2} + x - y + 1

a^{2} - 3 a + 1 = 0

u^{2} = 0

What are the solutions to the equation 1/3 w^2+1/3 w=-1/4 ?
The solutions to the equation 1/3 w^2+1/3 w=-1/4 are w=-1/2+i(sqrt(2))/2 ,w=-1/2-i(sqrt(2))/2
Find the zeros of 1/3 w^2+1/3 w=-1/4
The zeros of 1/3 w^2+1/3 w=-1/4 are w=-1/2+i(sqrt(2))/2 ,w=-1/2-i(sqrt(2))/2