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

The solutions to the equation 1/2 x^2+x+1=0 are x=-1+i,x=-1-i

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

The zeros of 1/2 x^2+x+1=0 are x=-1+i,x=-1-i

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

x = - 1 + i, x = - 1 - i

Solution steps

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

Multiply both sides by

2

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

Solve with the quadratic formula

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

Simplify

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = - 1 + i, x = - 1 - i

y^{2} - 7 = 0

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

5 x^{2} + 6 x - 25 = 0

x, 2 x^{2} - 8 x + 5 = 0

lo g_{10} (9) (2 n^{2} - 14 n) = lo g_{10} (9) (- 45 + n^{2})

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