5x+4-3(2x-1)=8-(7x-1)x

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Solution for 5x+4-3(2x-1)=8-(7x-1)x equation:


Simplifying
5x + 4 + -3(2x + -1) = 8 + -1(7x + -1) * x

Reorder the terms:
5x + 4 + -3(-1 + 2x) = 8 + -1(7x + -1) * x
5x + 4 + (-1 * -3 + 2x * -3) = 8 + -1(7x + -1) * x
5x + 4 + (3 + -6x) = 8 + -1(7x + -1) * x

Reorder the terms:
4 + 3 + 5x + -6x = 8 + -1(7x + -1) * x

Combine like terms: 4 + 3 = 7
7 + 5x + -6x = 8 + -1(7x + -1) * x

Combine like terms: 5x + -6x = -1x
7 + -1x = 8 + -1(7x + -1) * x

Reorder the terms:
7 + -1x = 8 + -1(-1 + 7x) * x

Reorder the terms for easier multiplication:
7 + -1x = 8 + -1x(-1 + 7x)
7 + -1x = 8 + (-1 * -1x + 7x * -1x)
7 + -1x = 8 + (1x + -7x2)

Solving
7 + -1x = 8 + 1x + -7x2

Solving for variable 'x'.

Reorder the terms:
7 + -8 + -1x + -1x + 7x2 = 8 + 1x + -7x2 + -8 + -1x + 7x2

Combine like terms: 7 + -8 = -1
-1 + -1x + -1x + 7x2 = 8 + 1x + -7x2 + -8 + -1x + 7x2

Combine like terms: -1x + -1x = -2x
-1 + -2x + 7x2 = 8 + 1x + -7x2 + -8 + -1x + 7x2

Reorder the terms:
-1 + -2x + 7x2 = 8 + -8 + 1x + -1x + -7x2 + 7x2

Combine like terms: 8 + -8 = 0
-1 + -2x + 7x2 = 0 + 1x + -1x + -7x2 + 7x2
-1 + -2x + 7x2 = 1x + -1x + -7x2 + 7x2

Combine like terms: 1x + -1x = 0
-1 + -2x + 7x2 = 0 + -7x2 + 7x2
-1 + -2x + 7x2 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
-1 + -2x + 7x2 = 0

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

Divide each side by '7'.
-0.1428571429 + -0.2857142857x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + -0.2857142857x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + -0.2857142857x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + -0.2857142857x + x2 = 0 + 0.1428571429
-0.2857142857x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
-0.2857142857x + x2 = 0.1428571429

The x term is -0.2857142857x.  Take half its coefficient (-0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
-0.2857142857x + 0.02040816328 + x2 = 0.1428571429 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857x + x2 = 0.1428571429 + 0.02040816328

Combine like terms: 0.1428571429 + 0.02040816328 = 0.16326530618
0.02040816328 + -0.2857142857x + x2 = 0.16326530618

Factor a perfect square on the left side:
(x + -0.1428571429)(x + -0.1428571429) = 0.16326530618

Calculate the square root of the right side: 0.404061018

Break this problem into two subproblems by setting 
(x + -0.1428571429) equal to 0.404061018 and -0.404061018.

Subproblem 1

x + -0.1428571429 = 0.404061018 Simplifying x + -0.1428571429 = 0.404061018 Reorder the terms: -0.1428571429 + x = 0.404061018 Solving -0.1428571429 + x = 0.404061018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.404061018 + 0.1428571429 x = 0.404061018 + 0.1428571429 Combine like terms: 0.404061018 + 0.1428571429 = 0.5469181609 x = 0.5469181609 Simplifying x = 0.5469181609

Subproblem 2

x + -0.1428571429 = -0.404061018 Simplifying x + -0.1428571429 = -0.404061018 Reorder the terms: -0.1428571429 + x = -0.404061018 Solving -0.1428571429 + x = -0.404061018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.404061018 + 0.1428571429 x = -0.404061018 + 0.1428571429 Combine like terms: -0.404061018 + 0.1428571429 = -0.2612038751 x = -0.2612038751 Simplifying x = -0.2612038751

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5469181609, -0.2612038751}

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