What are the solutions to the equation 2x^2+x+0.5=0 ?

The solutions to the equation 2x^2+x+0.5=0 are x=-1/4+i(sqrt(3))/4 ,x=-1/4-i(sqrt(3))/4

Find the zeros of 2x^2+x+0.5=0

The zeros of 2x^2+x+0.5=0 are x=-1/4+i(sqrt(3))/4 ,x=-1/4-i(sqrt(3))/4

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2 x^{2} + x + 0.5 = 0

x = - \frac{1}{4} + i \frac{3}{4}, x = - \frac{1}{4} - i \frac{3}{4}

Solution steps

2 x^{2} + x + 0.5 = 0

Multiply both sides by

10

20 x^{2} + 10 x + 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 10 \pm 1 0 ^{2} - 4 \cdot 20 \cdot 5}{2 \cdot 20}

Simplify

1 0^{2} - 4 \cdot 20 \cdot 5 : 103 i

x_{1, 2} = \frac{- 10 \pm 10 3 i}{2 \cdot 20}

Separate the solutions

x_{1} = \frac{- 10 + 10 3 i}{2 \cdot 20}, x_{2} = \frac{- 10 - 10 3 i}{2 \cdot 20}

x = \frac{- 10 + 10 3 i}{2 \cdot 20} : - \frac{1}{4} + i \frac{3}{4}

x = \frac{- 10 - 10 3 i}{2 \cdot 20} : - \frac{1}{4} - i \frac{3}{4}

The solutions to the quadratic equation are:

x = - \frac{1}{4} + i \frac{3}{4}, x = - \frac{1}{4} - i \frac{3}{4}

5 x + x^{2} = 0

(1 - x) (1 - x) - 1 = 0

(x - 5)^{2} + 4 (x - 5) + 4 = 0

X, X^{2} - Y^{2} + 4 Y - 4 = 0

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

What are the solutions to the equation 2x^2+x+0.5=0 ?
The solutions to the equation 2x^2+x+0.5=0 are x=-1/4+i(sqrt(3))/4 ,x=-1/4-i(sqrt(3))/4
Find the zeros of 2x^2+x+0.5=0
The zeros of 2x^2+x+0.5=0 are x=-1/4+i(sqrt(3))/4 ,x=-1/4-i(sqrt(3))/4