2-3(4-x)=5(2-x)4x

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Solution for 2-3(4-x)=5(2-x)4x equation:


Simplifying
2 + -3(4 + -1x) = 5(2 + -1x) * 4x
2 + (4 * -3 + -1x * -3) = 5(2 + -1x) * 4x
2 + (-12 + 3x) = 5(2 + -1x) * 4x

Combine like terms: 2 + -12 = -10
-10 + 3x = 5(2 + -1x) * 4x

Reorder the terms for easier multiplication:
-10 + 3x = 5 * 4x(2 + -1x)

Multiply 5 * 4
-10 + 3x = 20x(2 + -1x)
-10 + 3x = (2 * 20x + -1x * 20x)
-10 + 3x = (40x + -20x2)

Solving
-10 + 3x = 40x + -20x2

Solving for variable 'x'.

Combine like terms: 3x + -40x = -37x
-10 + -37x + 20x2 = 40x + -20x2 + -40x + 20x2

Reorder the terms:
-10 + -37x + 20x2 = 40x + -40x + -20x2 + 20x2

Combine like terms: 40x + -40x = 0
-10 + -37x + 20x2 = 0 + -20x2 + 20x2
-10 + -37x + 20x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
-10 + -37x + 20x2 = 0

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

Divide each side by '20'.
-0.5 + -1.85x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.85x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.85x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.85x + x2 = 0 + 0.5
-1.85x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1.85x + x2 = 0.5

The x term is -1.85x.  Take half its coefficient (-0.925).
Square it (0.855625) and add it to both sides.

Add '0.855625' to each side of the equation.
-1.85x + 0.855625 + x2 = 0.5 + 0.855625

Reorder the terms:
0.855625 + -1.85x + x2 = 0.5 + 0.855625

Combine like terms: 0.5 + 0.855625 = 1.355625
0.855625 + -1.85x + x2 = 1.355625

Factor a perfect square on the left side:
(x + -0.925)(x + -0.925) = 1.355625

Calculate the square root of the right side: 1.164313102

Break this problem into two subproblems by setting 
(x + -0.925) equal to 1.164313102 and -1.164313102.

Subproblem 1

x + -0.925 = 1.164313102 Simplifying x + -0.925 = 1.164313102 Reorder the terms: -0.925 + x = 1.164313102 Solving -0.925 + x = 1.164313102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.925' to each side of the equation. -0.925 + 0.925 + x = 1.164313102 + 0.925 Combine like terms: -0.925 + 0.925 = 0.000 0.000 + x = 1.164313102 + 0.925 x = 1.164313102 + 0.925 Combine like terms: 1.164313102 + 0.925 = 2.089313102 x = 2.089313102 Simplifying x = 2.089313102

Subproblem 2

x + -0.925 = -1.164313102 Simplifying x + -0.925 = -1.164313102 Reorder the terms: -0.925 + x = -1.164313102 Solving -0.925 + x = -1.164313102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.925' to each side of the equation. -0.925 + 0.925 + x = -1.164313102 + 0.925 Combine like terms: -0.925 + 0.925 = 0.000 0.000 + x = -1.164313102 + 0.925 x = -1.164313102 + 0.925 Combine like terms: -1.164313102 + 0.925 = -0.239313102 x = -0.239313102 Simplifying x = -0.239313102

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.089313102, -0.239313102}

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