-2x(x-2)-4=3(x+1)-9x

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Solution for -2x(x-2)-4=3(x+1)-9x equation:


Simplifying
-2x(x + -2) + -4 = 3(x + 1) + -9x

Reorder the terms:
-2x(-2 + x) + -4 = 3(x + 1) + -9x
(-2 * -2x + x * -2x) + -4 = 3(x + 1) + -9x
(4x + -2x2) + -4 = 3(x + 1) + -9x

Reorder the terms:
-4 + 4x + -2x2 = 3(x + 1) + -9x

Reorder the terms:
-4 + 4x + -2x2 = 3(1 + x) + -9x
-4 + 4x + -2x2 = (1 * 3 + x * 3) + -9x
-4 + 4x + -2x2 = (3 + 3x) + -9x

Combine like terms: 3x + -9x = -6x
-4 + 4x + -2x2 = 3 + -6x

Solving
-4 + 4x + -2x2 = 3 + -6x

Solving for variable 'x'.

Reorder the terms:
-4 + -3 + 4x + 6x + -2x2 = 3 + -6x + -3 + 6x

Combine like terms: -4 + -3 = -7
-7 + 4x + 6x + -2x2 = 3 + -6x + -3 + 6x

Combine like terms: 4x + 6x = 10x
-7 + 10x + -2x2 = 3 + -6x + -3 + 6x

Reorder the terms:
-7 + 10x + -2x2 = 3 + -3 + -6x + 6x

Combine like terms: 3 + -3 = 0
-7 + 10x + -2x2 = 0 + -6x + 6x
-7 + 10x + -2x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-7 + 10x + -2x2 = 0

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

Divide each side by '-2'.
3.5 + -5x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -5x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -5x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -5x + x2 = 0 + -3.5
-5x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-5x + x2 = -3.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -3.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -3.5 + 6.25

Combine like terms: -3.5 + 6.25 = 2.75
6.25 + -5x + x2 = 2.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

x + -2.5 = 1.658312395 Simplifying x + -2.5 = 1.658312395 Reorder the terms: -2.5 + x = 1.658312395 Solving -2.5 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.658312395 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.658312395 + 2.5 x = 1.658312395 + 2.5 Combine like terms: 1.658312395 + 2.5 = 4.158312395 x = 4.158312395 Simplifying x = 4.158312395

Subproblem 2

x + -2.5 = -1.658312395 Simplifying x + -2.5 = -1.658312395 Reorder the terms: -2.5 + x = -1.658312395 Solving -2.5 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.658312395 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.658312395 + 2.5 x = -1.658312395 + 2.5 Combine like terms: -1.658312395 + 2.5 = 0.841687605 x = 0.841687605 Simplifying x = 0.841687605

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.158312395, 0.841687605}

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