-7x(2x-1)=35

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Solution for -7x(2x-1)=35 equation: 


Simplifying
-7x(2x + -1) = 35

Reorder the terms:
-7x(-1 + 2x) = 35
(-1 * -7x + 2x * -7x) = 35
(7x + -14x2) = 35

Solving
7x + -14x2 = 35

Solving for variable 'x'.

Reorder the terms:
-35 + 7x + -14x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + 7x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-5 + x + -2x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-5 + x + -2x2)' equal to zero and attempt to solve:

Simplifying
-5 + x + -2x2 = 0

Solving
-5 + x + -2x2 = 0

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

Divide each side by '-2'.
2.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -0.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -0.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -0.5x + x2 = 0 + -2.5
-0.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-0.5x + x2 = -2.5

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 = -2.5 + 0.25

Reorder the terms:
0.25 + -0.5x + x2 = -2.5 + 0.25

Combine like terms: -2.5 + 0.25 = -2.25
0.25 + -0.5x + x2 = -2.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -2.25

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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