What are the solutions to the equation 1/2 x^2+x+4=0 ?

The solutions to the equation 1/2 x^2+x+4=0 are x=-1+sqrt(7)i,x=-1-sqrt(7)i

Find the zeros of 1/2 x^2+x+4=0

The zeros of 1/2 x^2+x+4=0 are x=-1+sqrt(7)i,x=-1-sqrt(7)i

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\frac{1}{2} x^{2} + x + 4 = 0

x = - 1 + 7 i, x = - 1 - 7 i

Solution steps

\frac{1}{2} x^{2} + x + 4 = 0

Multiply both sides by

2

x^{2} + 2 x + 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 1 \cdot 8}{2 \cdot 1}

Simplify

2^{2} - 4 \cdot 1 \cdot 8 : 27 i

x_{1, 2} = \frac{- 2 \pm 2 7 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 2 + 2 7 i}{2 \cdot 1}, x_{2} = \frac{- 2 - 2 7 i}{2 \cdot 1}

x = \frac{- 2 + 2 7 i}{2 \cdot 1} : - 1 + 7 i

x = \frac{- 2 - 2 7 i}{2 \cdot 1} : - 1 - 7 i

The solutions to the quadratic equation are:

x = - 1 + 7 i, x = - 1 - 7 i

4 x^{2} = 8 x - 1

- 3 = \frac{1 2 ^{2}}{20} - \frac{10}{2 \cdot 1 2 ^{2}} \cdot x^{2}

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

4 1^{2} = x^{2} + 4 0^{2}

x^{2} - x = - \frac{1}{4}

What are the solutions to the equation 1/2 x^2+x+4=0 ?
The solutions to the equation 1/2 x^2+x+4=0 are x=-1+sqrt(7)i,x=-1-sqrt(7)i
Find the zeros of 1/2 x^2+x+4=0
The zeros of 1/2 x^2+x+4=0 are x=-1+sqrt(7)i,x=-1-sqrt(7)i