4x(x-2)-6x=35

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Solution for 4x(x-2)-6x=35 equation:


Simplifying
4x(x + -2) + -6x = 35

Reorder the terms:
4x(-2 + x) + -6x = 35
(-2 * 4x + x * 4x) + -6x = 35
(-8x + 4x2) + -6x = 35

Reorder the terms:
-8x + -6x + 4x2 = 35

Combine like terms: -8x + -6x = -14x
-14x + 4x2 = 35

Solving
-14x + 4x2 = 35

Solving for variable 'x'.

Reorder the terms:
-35 + -14x + 4x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + -14x + 4x2 = 0

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

Divide each side by '4'.
-8.75 + -3.5x + x2 = 0

Move the constant term to the right:

Add '8.75' to each side of the equation.
-8.75 + -3.5x + 8.75 + x2 = 0 + 8.75

Reorder the terms:
-8.75 + 8.75 + -3.5x + x2 = 0 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + -3.5x + x2 = 0 + 8.75
-3.5x + x2 = 0 + 8.75

Combine like terms: 0 + 8.75 = 8.75
-3.5x + x2 = 8.75

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 8.75 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 8.75 + 3.0625

Combine like terms: 8.75 + 3.0625 = 11.8125
3.0625 + -3.5x + x2 = 11.8125

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 11.8125

Calculate the square root of the right side: 3.436931771

Break this problem into two subproblems by setting 
(x + -1.75) equal to 3.436931771 and -3.436931771.

Subproblem 1

x + -1.75 = 3.436931771 Simplifying x + -1.75 = 3.436931771 Reorder the terms: -1.75 + x = 3.436931771 Solving -1.75 + x = 3.436931771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.436931771 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.436931771 + 1.75 x = 3.436931771 + 1.75 Combine like terms: 3.436931771 + 1.75 = 5.186931771 x = 5.186931771 Simplifying x = 5.186931771

Subproblem 2

x + -1.75 = -3.436931771 Simplifying x + -1.75 = -3.436931771 Reorder the terms: -1.75 + x = -3.436931771 Solving -1.75 + x = -3.436931771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.436931771 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.436931771 + 1.75 x = -3.436931771 + 1.75 Combine like terms: -3.436931771 + 1.75 = -1.686931771 x = -1.686931771 Simplifying x = -1.686931771

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.186931771, -1.686931771}

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