0.2x^2-2x+0.6x-6=x^2-0.2x+3x-0.6

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Solution for 0.2x^2-2x+0.6x-6=x^2-0.2x+3x-0.6 equation:


Simplifying
0.2x2 + -2x + 0.6x + -6 = x2 + -0.2x + 3x + -0.6

Reorder the terms:
-6 + -2x + 0.6x + 0.2x2 = x2 + -0.2x + 3x + -0.6

Combine like terms: -2x + 0.6x = -1.4x
-6 + -1.4x + 0.2x2 = x2 + -0.2x + 3x + -0.6

Reorder the terms:
-6 + -1.4x + 0.2x2 = -0.6 + -0.2x + 3x + x2

Combine like terms: -0.2x + 3x = 2.8x
-6 + -1.4x + 0.2x2 = -0.6 + 2.8x + x2

Solving
-6 + -1.4x + 0.2x2 = -0.6 + 2.8x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 0.6 + -1.4x + -2.8x + 0.2x2 + -1x2 = -0.6 + 2.8x + x2 + 0.6 + -2.8x + -1x2

Combine like terms: -6 + 0.6 = -5.4
-5.4 + -1.4x + -2.8x + 0.2x2 + -1x2 = -0.6 + 2.8x + x2 + 0.6 + -2.8x + -1x2

Combine like terms: -1.4x + -2.8x = -4.2x
-5.4 + -4.2x + 0.2x2 + -1x2 = -0.6 + 2.8x + x2 + 0.6 + -2.8x + -1x2

Combine like terms: 0.2x2 + -1x2 = -0.8x2
-5.4 + -4.2x + -0.8x2 = -0.6 + 2.8x + x2 + 0.6 + -2.8x + -1x2

Reorder the terms:
-5.4 + -4.2x + -0.8x2 = -0.6 + 0.6 + 2.8x + -2.8x + x2 + -1x2

Combine like terms: -0.6 + 0.6 = 0.0
-5.4 + -4.2x + -0.8x2 = 0.0 + 2.8x + -2.8x + x2 + -1x2
-5.4 + -4.2x + -0.8x2 = 2.8x + -2.8x + x2 + -1x2

Combine like terms: 2.8x + -2.8x = 0.0
-5.4 + -4.2x + -0.8x2 = 0.0 + x2 + -1x2
-5.4 + -4.2x + -0.8x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5.4 + -4.2x + -0.8x2 = 0

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
6.75 + 5.25x + x2 = 0

Move the constant term to the right:

Add '-6.75' to each side of the equation.
6.75 + 5.25x + -6.75 + x2 = 0 + -6.75

Reorder the terms:
6.75 + -6.75 + 5.25x + x2 = 0 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + 5.25x + x2 = 0 + -6.75
5.25x + x2 = 0 + -6.75

Combine like terms: 0 + -6.75 = -6.75
5.25x + x2 = -6.75

The x term is 5.25x.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25x + 6.890625 + x2 = -6.75 + 6.890625

Reorder the terms:
6.890625 + 5.25x + x2 = -6.75 + 6.890625

Combine like terms: -6.75 + 6.890625 = 0.140625
6.890625 + 5.25x + x2 = 0.140625

Factor a perfect square on the left side:
(x + 2.625)(x + 2.625) = 0.140625

Calculate the square root of the right side: 0.375

Break this problem into two subproblems by setting 
(x + 2.625) equal to 0.375 and -0.375.

Subproblem 1

x + 2.625 = 0.375 Simplifying x + 2.625 = 0.375 Reorder the terms: 2.625 + x = 0.375 Solving 2.625 + x = 0.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 0.375 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 0.375 + -2.625 x = 0.375 + -2.625 Combine like terms: 0.375 + -2.625 = -2.25 x = -2.25 Simplifying x = -2.25

Subproblem 2

x + 2.625 = -0.375 Simplifying x + 2.625 = -0.375 Reorder the terms: 2.625 + x = -0.375 Solving 2.625 + x = -0.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -0.375 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -0.375 + -2.625 x = -0.375 + -2.625 Combine like terms: -0.375 + -2.625 = -3 x = -3 Simplifying x = -3

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.25, -3}

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