4x^2+6x+54=0

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Solution for 4x^2+6x+54=0 equation: 


Simplifying
4x2 + 6x + 54 = 0

Reorder the terms:
54 + 6x + 4x2 = 0

Solving
54 + 6x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + 3x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(27 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
27 + 3x + 2x2 = 0

Solving
27 + 3x + 2x2 = 0

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

Divide each side by '2'.
13.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + 1.5x + -13.5 + x2 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + 1.5x + x2 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + 1.5x + x2 = 0 + -13.5
1.5x + x2 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
1.5x + x2 = -13.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -13.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -13.5 + 0.5625

Combine like terms: -13.5 + 0.5625 = -12.9375
0.5625 + 1.5x + x2 = -12.9375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -12.9375

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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