4x^2-2x+3x+6=0

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Solution for 4x^2-2x+3x+6=0 equation:


Simplifying
4x2 + -2x + 3x + 6 = 0

Reorder the terms:
6 + -2x + 3x + 4x2 = 0

Combine like terms: -2x + 3x = 1x
6 + 1x + 4x2 = 0

Solving
6 + 1x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
1.5 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.25x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.25x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.25x + x2 = 0 + -1.5
0.25x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.25x + x2 = -1.5

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = -1.5 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = -1.5 + 0.015625

Combine like terms: -1.5 + 0.015625 = -1.484375
0.015625 + 0.25x + x2 = -1.484375

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = -1.484375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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