6-4x(2x-1)=34

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Solution for 6-4x(2x-1)=34 equation: 


Simplifying
6 + -4x(2x + -1) = 34

Reorder the terms:
6 + -4x(-1 + 2x) = 34
6 + (-1 * -4x + 2x * -4x) = 34
6 + (4x + -8x2) = 34

Solving
6 + 4x + -8x2 = 34

Solving for variable 'x'.

Reorder the terms:
6 + -34 + 4x + -8x2 = 34 + -34

Combine like terms: 6 + -34 = -28
-28 + 4x + -8x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-28 + 4x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + x + -2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + x + -2x2)' equal to zero and attempt to solve:

Simplifying
-7 + x + -2x2 = 0

Solving
-7 + x + -2x2 = 0

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

Divide each side by '-2'.
3.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -0.5x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -0.5x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -0.5x + x2 = 0 + -3.5
-0.5x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-0.5x + x2 = -3.5

The x term is x.  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.
-0.5x + 0.25 + x2 = -3.5 + 0.25

Reorder the terms:
0.25 + -0.5x + x2 = -3.5 + 0.25

Combine like terms: -3.5 + 0.25 = -3.25
0.25 + -0.5x + x2 = -3.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -3.25

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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