(5-3x)-(-4x+6)=(8x+11)-3x(3x-6)

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Solution for (5-3x)-(-4x+6)=(8x+11)-3x(3x-6) equation:


Simplifying
(5 + -3x) + -1(-4x + 6) = (8x + 11) + -3x(3x + -6)

Remove parenthesis around (5 + -3x)
5 + -3x + -1(-4x + 6) = (8x + 11) + -3x(3x + -6)

Reorder the terms:
5 + -3x + -1(6 + -4x) = (8x + 11) + -3x(3x + -6)
5 + -3x + (6 * -1 + -4x * -1) = (8x + 11) + -3x(3x + -6)
5 + -3x + (-6 + 4x) = (8x + 11) + -3x(3x + -6)

Reorder the terms:
5 + -6 + -3x + 4x = (8x + 11) + -3x(3x + -6)

Combine like terms: 5 + -6 = -1
-1 + -3x + 4x = (8x + 11) + -3x(3x + -6)

Combine like terms: -3x + 4x = 1x
-1 + 1x = (8x + 11) + -3x(3x + -6)

Reorder the terms:
-1 + 1x = (11 + 8x) + -3x(3x + -6)

Remove parenthesis around (11 + 8x)
-1 + 1x = 11 + 8x + -3x(3x + -6)

Reorder the terms:
-1 + 1x = 11 + 8x + -3x(-6 + 3x)
-1 + 1x = 11 + 8x + (-6 * -3x + 3x * -3x)
-1 + 1x = 11 + 8x + (18x + -9x2)

Combine like terms: 8x + 18x = 26x
-1 + 1x = 11 + 26x + -9x2

Solving
-1 + 1x = 11 + 26x + -9x2

Solving for variable 'x'.

Reorder the terms:
-1 + -11 + 1x + -26x + 9x2 = 11 + 26x + -9x2 + -11 + -26x + 9x2

Combine like terms: -1 + -11 = -12
-12 + 1x + -26x + 9x2 = 11 + 26x + -9x2 + -11 + -26x + 9x2

Combine like terms: 1x + -26x = -25x
-12 + -25x + 9x2 = 11 + 26x + -9x2 + -11 + -26x + 9x2

Reorder the terms:
-12 + -25x + 9x2 = 11 + -11 + 26x + -26x + -9x2 + 9x2

Combine like terms: 11 + -11 = 0
-12 + -25x + 9x2 = 0 + 26x + -26x + -9x2 + 9x2
-12 + -25x + 9x2 = 26x + -26x + -9x2 + 9x2

Combine like terms: 26x + -26x = 0
-12 + -25x + 9x2 = 0 + -9x2 + 9x2
-12 + -25x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-12 + -25x + 9x2 = 0

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

Divide each side by '9'.
-1.333333333 + -2.777777778x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -2.777777778x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -2.777777778x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -2.777777778x + x2 = 0 + 1.333333333
-2.777777778x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-2.777777778x + x2 = 1.333333333

The x term is -2.777777778x.  Take half its coefficient (-1.388888889).
Square it (1.929012346) and add it to both sides.

Add '1.929012346' to each side of the equation.
-2.777777778x + 1.929012346 + x2 = 1.333333333 + 1.929012346

Reorder the terms:
1.929012346 + -2.777777778x + x2 = 1.333333333 + 1.929012346

Combine like terms: 1.333333333 + 1.929012346 = 3.262345679
1.929012346 + -2.777777778x + x2 = 3.262345679

Factor a perfect square on the left side:
(x + -1.388888889)(x + -1.388888889) = 3.262345679

Calculate the square root of the right side: 1.806196467

Break this problem into two subproblems by setting 
(x + -1.388888889) equal to 1.806196467 and -1.806196467.

Subproblem 1

x + -1.388888889 = 1.806196467 Simplifying x + -1.388888889 = 1.806196467 Reorder the terms: -1.388888889 + x = 1.806196467 Solving -1.388888889 + x = 1.806196467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = 1.806196467 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = 1.806196467 + 1.388888889 x = 1.806196467 + 1.388888889 Combine like terms: 1.806196467 + 1.388888889 = 3.195085356 x = 3.195085356 Simplifying x = 3.195085356

Subproblem 2

x + -1.388888889 = -1.806196467 Simplifying x + -1.388888889 = -1.806196467 Reorder the terms: -1.388888889 + x = -1.806196467 Solving -1.388888889 + x = -1.806196467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = -1.806196467 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = -1.806196467 + 1.388888889 x = -1.806196467 + 1.388888889 Combine like terms: -1.806196467 + 1.388888889 = -0.417307578 x = -0.417307578 Simplifying x = -0.417307578

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.195085356, -0.417307578}

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