243x^2-90x+36=0

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Solution for 243x^2-90x+36=0 equation: 


Simplifying
243x2 + -90x + 36 = 0

Reorder the terms:
36 + -90x + 243x2 = 0

Solving
36 + -90x + 243x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(4 + -10x + 27x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(4 + -10x + 27x2)' equal to zero and attempt to solve:

Simplifying
4 + -10x + 27x2 = 0

Solving
4 + -10x + 27x2 = 0

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

Divide each side by '27'.
0.1481481481 + -0.3703703704x + x2 = 0

Move the constant term to the right:

Add '-0.1481481481' to each side of the equation.
0.1481481481 + -0.3703703704x + -0.1481481481 + x2 = 0 + -0.1481481481

Reorder the terms:
0.1481481481 + -0.1481481481 + -0.3703703704x + x2 = 0 + -0.1481481481

Combine like terms: 0.1481481481 + -0.1481481481 = 0.0000000000
0.0000000000 + -0.3703703704x + x2 = 0 + -0.1481481481
-0.3703703704x + x2 = 0 + -0.1481481481

Combine like terms: 0 + -0.1481481481 = -0.1481481481
-0.3703703704x + x2 = -0.1481481481

The x term is -0.3703703704x.  Take half its coefficient (-0.1851851852).
Square it (0.03429355282) and add it to both sides.

Add '0.03429355282' to each side of the equation.
-0.3703703704x + 0.03429355282 + x2 = -0.1481481481 + 0.03429355282

Reorder the terms:
0.03429355282 + -0.3703703704x + x2 = -0.1481481481 + 0.03429355282

Combine like terms: -0.1481481481 + 0.03429355282 = -0.11385459528
0.03429355282 + -0.3703703704x + x2 = -0.11385459528

Factor a perfect square on the left side:
(x + -0.1851851852)(x + -0.1851851852) = -0.11385459528

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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