27=25+4x-4x^2

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Solution for 27=25+4x-4x^2 equation: 


Simplifying
27 = 25 + 4x + -4x2

Solving
27 = 25 + 4x + -4x2

Solving for variable 'x'.

Combine like terms: 27 + -25 = 2
2 + -4x + 4x2 = 25 + 4x + -4x2 + -25 + -4x + 4x2

Reorder the terms:
2 + -4x + 4x2 = 25 + -25 + 4x + -4x + -4x2 + 4x2

Combine like terms: 25 + -25 = 0
2 + -4x + 4x2 = 0 + 4x + -4x + -4x2 + 4x2
2 + -4x + 4x2 = 4x + -4x + -4x2 + 4x2

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

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

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

Ignore the factor 2.

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

Simplifying
1 + -2x + 2x2 = 0

Solving
1 + -2x + 2x2 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1x + x2 = 0 + -0.5
-1x + x2 = 0 + -0.5

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

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + -1x + x2 = -0.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -0.25

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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