144x^2+216x+210=0

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Solution for 144x^2+216x+210=0 equation: 


Simplifying
144x2 + 216x + 210 = 0

Reorder the terms:
210 + 216x + 144x2 = 0

Solving
210 + 216x + 144x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(35 + 36x + 24x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(35 + 36x + 24x2)' equal to zero and attempt to solve:

Simplifying
35 + 36x + 24x2 = 0

Solving
35 + 36x + 24x2 = 0

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

Divide each side by '24'.
1.458333333 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-1.458333333' to each side of the equation.
1.458333333 + 1.5x + -1.458333333 + x2 = 0 + -1.458333333

Reorder the terms:
1.458333333 + -1.458333333 + 1.5x + x2 = 0 + -1.458333333

Combine like terms: 1.458333333 + -1.458333333 = 0.000000000
0.000000000 + 1.5x + x2 = 0 + -1.458333333
1.5x + x2 = 0 + -1.458333333

Combine like terms: 0 + -1.458333333 = -1.458333333
1.5x + x2 = -1.458333333

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 = -1.458333333 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -1.458333333 + 0.5625

Combine like terms: -1.458333333 + 0.5625 = -0.895833333
0.5625 + 1.5x + x2 = -0.895833333

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -0.895833333

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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