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

The solutions to the equation x^2+1/2 x+1=0 are x=-1/4+i(sqrt(15))/4 ,x=-1/4-i(sqrt(15))/4

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

The zeros of x^2+1/2 x+1=0 are x=-1/4+i(sqrt(15))/4 ,x=-1/4-i(sqrt(15))/4

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

x = - \frac{1}{4} + i \frac{15}{4}, x = - \frac{1}{4} - i \frac{15}{4}

Solution steps

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

Multiply both sides by

2

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

Solve with the quadratic formula

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

Simplify

1^{2} - 4 \cdot 2 \cdot 2 : 15 i

x_{1, 2} = \frac{- 1 \pm 15 i}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 1 + 15 i}{2 \cdot 2}, x_{2} = \frac{- 1 - 15 i}{2 \cdot 2}

x = \frac{- 1 + 15 i}{2 \cdot 2} : - \frac{1}{4} + i \frac{15}{4}

x = \frac{- 1 - 15 i}{2 \cdot 2} : - \frac{1}{4} - i \frac{15}{4}

The solutions to the quadratic equation are:

x = - \frac{1}{4} + i \frac{15}{4}, x = - \frac{1}{4} - i \frac{15}{4}

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

4 x^{2} + 16 x + 3 = 8 x

x^{2} - 8 x - 63 = - 10 x

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

x, y^{3} + y^{2} - 5 y - x^{2} = - 4

What are the solutions to the equation x^2+1/2 x+1=0 ?
The solutions to the equation x^2+1/2 x+1=0 are x=-1/4+i(sqrt(15))/4 ,x=-1/4-i(sqrt(15))/4
Find the zeros of x^2+1/2 x+1=0
The zeros of x^2+1/2 x+1=0 are x=-1/4+i(sqrt(15))/4 ,x=-1/4-i(sqrt(15))/4