# Solve for x: 2x^2 - 2x+5=0

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### 2 Answers

The equation to be solved is : 2x^2 - 2x + 5 = 0

2x^2 - 2x + 5 = 0

x1 = 2/4 + sqrt (4 - 40) / 4

=> 1/2 + i*sqrt 36 / 4

=> 1/2 + i*6/4

=> 1/2 + (3/2)i

x2 = 1/2 - (3/2)i

**The solution of the equation is x = 1/2 + (3/2)i and x = 1/2 - (3/2)i**

Since it is a quadratic equtaion, we'll apply quadratic formula to determine it's roots.

x1 = [-b + sqrt(b^2 - 4ac)]/2a

x1 = [2 + sqrt(4 - 4*2*5)]/4

x1 = (2+sqrt-36)/4

But sqrt(-36) = sqrt(-1)*36

sqrt -1 = i

sqrt(-36) = 6i or sqrt(-36) = -6i

x1 = (2+6i)/4

x1 = 1/2 + 3i/2

The other root is the conjugate of x1, x2 = 1/2 - 3i/2.

**The complex roots of the equation are: {1/2 - 3i/2; 1/2 + 3i/2}.**