-6x+2x-11=-2x(2x-3)+4

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Solution for -6x+2x-11=-2x(2x-3)+4 equation:


Simplifying
-6x + 2x + -11 = -2x(2x + -3) + 4

Reorder the terms:
-11 + -6x + 2x = -2x(2x + -3) + 4

Combine like terms: -6x + 2x = -4x
-11 + -4x = -2x(2x + -3) + 4

Reorder the terms:
-11 + -4x = -2x(-3 + 2x) + 4
-11 + -4x = (-3 * -2x + 2x * -2x) + 4
-11 + -4x = (6x + -4x2) + 4

Reorder the terms:
-11 + -4x = 4 + 6x + -4x2

Solving
-11 + -4x = 4 + 6x + -4x2

Solving for variable 'x'.

Reorder the terms:
-11 + -4 + -4x + -6x + 4x2 = 4 + 6x + -4x2 + -4 + -6x + 4x2

Combine like terms: -11 + -4 = -15
-15 + -4x + -6x + 4x2 = 4 + 6x + -4x2 + -4 + -6x + 4x2

Combine like terms: -4x + -6x = -10x
-15 + -10x + 4x2 = 4 + 6x + -4x2 + -4 + -6x + 4x2

Reorder the terms:
-15 + -10x + 4x2 = 4 + -4 + 6x + -6x + -4x2 + 4x2

Combine like terms: 4 + -4 = 0
-15 + -10x + 4x2 = 0 + 6x + -6x + -4x2 + 4x2
-15 + -10x + 4x2 = 6x + -6x + -4x2 + 4x2

Combine like terms: 6x + -6x = 0
-15 + -10x + 4x2 = 0 + -4x2 + 4x2
-15 + -10x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-15 + -10x + 4x2 = 0

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

Divide each side by '4'.
-3.75 + -2.5x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -2.5x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -2.5x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -2.5x + x2 = 0 + 3.75
-2.5x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-2.5x + x2 = 3.75

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 3.75 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 3.75 + 1.5625

Combine like terms: 3.75 + 1.5625 = 5.3125
1.5625 + -2.5x + x2 = 5.3125

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 5.3125

Calculate the square root of the right side: 2.304886114

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.304886114 and -2.304886114.

Subproblem 1

x + -1.25 = 2.304886114 Simplifying x + -1.25 = 2.304886114 Reorder the terms: -1.25 + x = 2.304886114 Solving -1.25 + x = 2.304886114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.304886114 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.304886114 + 1.25 x = 2.304886114 + 1.25 Combine like terms: 2.304886114 + 1.25 = 3.554886114 x = 3.554886114 Simplifying x = 3.554886114

Subproblem 2

x + -1.25 = -2.304886114 Simplifying x + -1.25 = -2.304886114 Reorder the terms: -1.25 + x = -2.304886114 Solving -1.25 + x = -2.304886114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.304886114 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.304886114 + 1.25 x = -2.304886114 + 1.25 Combine like terms: -2.304886114 + 1.25 = -1.054886114 x = -1.054886114 Simplifying x = -1.054886114

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.554886114, -1.054886114}

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