3x+4x-2+2(3x-45)x-4=56

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Solution for 3x+4x-2+2(3x-45)x-4=56 equation:


Simplifying
3x + 4x + -2 + 2(3x + -45) * x + -4 = 56

Reorder the terms:
3x + 4x + -2 + 2(-45 + 3x) * x + -4 = 56

Reorder the terms for easier multiplication:
3x + 4x + -2 + 2x(-45 + 3x) + -4 = 56
3x + 4x + -2 + (-45 * 2x + 3x * 2x) + -4 = 56
3x + 4x + -2 + (-90x + 6x2) + -4 = 56

Reorder the terms:
-2 + -4 + 3x + 4x + -90x + 6x2 = 56

Combine like terms: -2 + -4 = -6
-6 + 3x + 4x + -90x + 6x2 = 56

Combine like terms: 3x + 4x = 7x
-6 + 7x + -90x + 6x2 = 56

Combine like terms: 7x + -90x = -83x
-6 + -83x + 6x2 = 56

Solving
-6 + -83x + 6x2 = 56

Solving for variable 'x'.

Reorder the terms:
-6 + -56 + -83x + 6x2 = 56 + -56

Combine like terms: -6 + -56 = -62
-62 + -83x + 6x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-62 + -83x + 6x2 = 0

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

Divide each side by '6'.
-10.33333333 + -13.83333333x + x2 = 0

Move the constant term to the right:

Add '10.33333333' to each side of the equation.
-10.33333333 + -13.83333333x + 10.33333333 + x2 = 0 + 10.33333333

Reorder the terms:
-10.33333333 + 10.33333333 + -13.83333333x + x2 = 0 + 10.33333333

Combine like terms: -10.33333333 + 10.33333333 = 0.00000000
0.00000000 + -13.83333333x + x2 = 0 + 10.33333333
-13.83333333x + x2 = 0 + 10.33333333

Combine like terms: 0 + 10.33333333 = 10.33333333
-13.83333333x + x2 = 10.33333333

The x term is -13.83333333x.  Take half its coefficient (-6.916666665).
Square it (47.84027775) and add it to both sides.

Add '47.84027775' to each side of the equation.
-13.83333333x + 47.84027775 + x2 = 10.33333333 + 47.84027775

Reorder the terms:
47.84027775 + -13.83333333x + x2 = 10.33333333 + 47.84027775

Combine like terms: 10.33333333 + 47.84027775 = 58.17361108
47.84027775 + -13.83333333x + x2 = 58.17361108

Factor a perfect square on the left side:
(x + -6.916666665)(x + -6.916666665) = 58.17361108

Calculate the square root of the right side: 7.627162715

Break this problem into two subproblems by setting 
(x + -6.916666665) equal to 7.627162715 and -7.627162715.

Subproblem 1

x + -6.916666665 = 7.627162715 Simplifying x + -6.916666665 = 7.627162715 Reorder the terms: -6.916666665 + x = 7.627162715 Solving -6.916666665 + x = 7.627162715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.916666665' to each side of the equation. -6.916666665 + 6.916666665 + x = 7.627162715 + 6.916666665 Combine like terms: -6.916666665 + 6.916666665 = 0.000000000 0.000000000 + x = 7.627162715 + 6.916666665 x = 7.627162715 + 6.916666665 Combine like terms: 7.627162715 + 6.916666665 = 14.54382938 x = 14.54382938 Simplifying x = 14.54382938

Subproblem 2

x + -6.916666665 = -7.627162715 Simplifying x + -6.916666665 = -7.627162715 Reorder the terms: -6.916666665 + x = -7.627162715 Solving -6.916666665 + x = -7.627162715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.916666665' to each side of the equation. -6.916666665 + 6.916666665 + x = -7.627162715 + 6.916666665 Combine like terms: -6.916666665 + 6.916666665 = 0.000000000 0.000000000 + x = -7.627162715 + 6.916666665 x = -7.627162715 + 6.916666665 Combine like terms: -7.627162715 + 6.916666665 = -0.71049605 x = -0.71049605 Simplifying x = -0.71049605

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.54382938, -0.71049605}

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