42x^2-69x+20=7x^2-x

Solution for 42x^2-69x+20=7x^2-x equation:

Simplifying
42x2 + -69x + 20 = 7x2 + -1x

Reorder the terms:
20 + -69x + 42x2 = 7x2 + -1x

Reorder the terms:
20 + -69x + 42x2 = -1x + 7x2

Solving
20 + -69x + 42x2 = -1x + 7x2

Solving for variable 'x'.

Reorder the terms:
20 + -69x + x + 42x2 + -7x2 = -1x + 7x2 + x + -7x2

Combine like terms: -69x + x = -68x
20 + -68x + 42x2 + -7x2 = -1x + 7x2 + x + -7x2

Combine like terms: 42x2 + -7x2 = 35x2
20 + -68x + 35x2 = -1x + 7x2 + x + -7x2

Reorder the terms:
20 + -68x + 35x2 = -1x + x + 7x2 + -7x2

Combine like terms: -1x + x = 0
20 + -68x + 35x2 = 0 + 7x2 + -7x2
20 + -68x + 35x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
20 + -68x + 35x2 = 0

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

Divide each side by '35'.
0.5714285714 + -1.942857143x + x2 = 0

Move the constant term to the right:

Add '-0.5714285714' to each side of the equation.
0.5714285714 + -1.942857143x + -0.5714285714 + x2 = 0 + -0.5714285714

Reorder the terms:
0.5714285714 + -0.5714285714 + -1.942857143x + x2 = 0 + -0.5714285714

Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000
0.0000000000 + -1.942857143x + x2 = 0 + -0.5714285714
-1.942857143x + x2 = 0 + -0.5714285714

Combine like terms: 0 + -0.5714285714 = -0.5714285714
-1.942857143x + x2 = -0.5714285714

The x term is -1.942857143x.  Take half its coefficient (-0.9714285715).
Square it (0.9436734695) and add it to both sides.

Add '0.9436734695' to each side of the equation.
-1.942857143x + 0.9436734695 + x2 = -0.5714285714 + 0.9436734695

Reorder the terms:
0.9436734695 + -1.942857143x + x2 = -0.5714285714 + 0.9436734695

Combine like terms: -0.5714285714 + 0.9436734695 = 0.3722448981
0.9436734695 + -1.942857143x + x2 = 0.3722448981

Factor a perfect square on the left side:
(x + -0.9714285715)(x + -0.9714285715) = 0.3722448981

Calculate the square root of the right side: 0.610118757

Break this problem into two subproblems by setting 
(x + -0.9714285715) equal to 0.610118757 and -0.610118757.

Subproblem 1
x + -0.9714285715 = 0.610118757

Simplifying
x + -0.9714285715 = 0.610118757

Reorder the terms:
-0.9714285715 + x = 0.610118757

Solving
-0.9714285715 + x = 0.610118757

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.9714285715' to each side of the equation.
-0.9714285715 + 0.9714285715 + x = 0.610118757 + 0.9714285715

Combine like terms: -0.9714285715 + 0.9714285715 = 0.0000000000
0.0000000000 + x = 0.610118757 + 0.9714285715
x = 0.610118757 + 0.9714285715

Combine like terms: 0.610118757 + 0.9714285715 = 1.5815473285
x = 1.5815473285

Simplifying
x = 1.5815473285

Subproblem 2
x + -0.9714285715 = -0.610118757

Simplifying
x + -0.9714285715 = -0.610118757

Reorder the terms:
-0.9714285715 + x = -0.610118757

Solving
-0.9714285715 + x = -0.610118757

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.9714285715' to each side of the equation.
-0.9714285715 + 0.9714285715 + x = -0.610118757 + 0.9714285715

Combine like terms: -0.9714285715 + 0.9714285715 = 0.0000000000
0.0000000000 + x = -0.610118757 + 0.9714285715
x = -0.610118757 + 0.9714285715

Combine like terms: -0.610118757 + 0.9714285715 = 0.3613098145
x = 0.3613098145

Simplifying
x = 0.3613098145

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5815473285, 0.3613098145}