2x^2+6x+13=0

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Solution for 2x^2+6x+13=0 equation:


Simplifying
2x2 + 6x + 13 = 0

Reorder the terms:
13 + 6x + 2x2 = 0

Solving
13 + 6x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
6.5 + 3x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + 3x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + 3x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + 3x + x2 = 0 + -6.5
3x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
3x + x2 = -6.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -6.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -6.5 + 2.25

Combine like terms: -6.5 + 2.25 = -4.25
2.25 + 3x + x2 = -4.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -4.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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