6x^2-3x+6=0

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


Simplifying
6x2 + -3x + 6 = 0

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

Solving
6 + -3x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -1x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x + 2x2 = 0

Solving
2 + -1x + 2x2 = 0

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

Divide each side by '2'.
1 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -0.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -0.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.5x + x2 = 0 + -1
-0.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-0.5x + x2 = -1

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -1 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -1 + 0.0625

Combine like terms: -1 + 0.0625 = -0.9375
0.0625 + -0.5x + x2 = -0.9375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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