175.00+550.00x*1.00x=35.000+1680.00x

Solution for 175.00+550.00x*1.00x=35.000+1680.00x equation:

Simplifying
175.00 + 550.00x * 1.00x = 35.000 + 1680.00x

Reorder the terms for easier multiplication:
175.00 + 550.00 * 1.00x * x = 35.000 + 1680.00x

Multiply 550.00 * 1.00
175.00 + 550x * x = 35.000 + 1680.00x

Multiply x * x
175.00 + 550x2 = 35.000 + 1680.00x

Solving
175.00 + 550x2 = 35.000 + 1680.00x

Solving for variable 'x'.

Reorder the terms:
175.00 + -35.000 + -1680.00x + 550x2 = 35.000 + 1680.00x + -35.000 + -1680.00x

Combine like terms: 175.00 + -35.000 = 140
140 + -1680.00x + 550x2 = 35.000 + 1680.00x + -35.000 + -1680.00x

Reorder the terms:
140 + -1680.00x + 550x2 = 35.000 + -35.000 + 1680.00x + -1680.00x

Combine like terms: 35.000 + -35.000 = 0.000
140 + -1680.00x + 550x2 = 0.000 + 1680.00x + -1680.00x
140 + -1680.00x + 550x2 = 1680.00x + -1680.00x

Combine like terms: 1680.00x + -1680.00x = 0.00
140 + -1680.00x + 550x2 = 0.00

Factor out the Greatest Common Factor (GCF), '10'.
10(14 + -168x + 55x2) = 0.00

Ignore the factor 10.
Subproblem 1
Set the factor '(14 + -168x + 55x2)' equal to zero and attempt to solve:

Simplifying
14 + -168x + 55x2 = 0

Solving
14 + -168x + 55x2 = 0

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

Divide each side by '55'.
0.2545454545 + -3.054545455x + x2 = 0

Move the constant term to the right:

Add '-0.2545454545' to each side of the equation.
0.2545454545 + -3.054545455x + -0.2545454545 + x2 = 0 + -0.2545454545

Reorder the terms:
0.2545454545 + -0.2545454545 + -3.054545455x + x2 = 0 + -0.2545454545

Combine like terms: 0.2545454545 + -0.2545454545 = 0.0000000000
0.0000000000 + -3.054545455x + x2 = 0 + -0.2545454545
-3.054545455x + x2 = 0 + -0.2545454545

Combine like terms: 0 + -0.2545454545 = -0.2545454545
-3.054545455x + x2 = -0.2545454545

The x term is -3.054545455x.  Take half its coefficient (-1.527272728).
Square it (2.332561986) and add it to both sides.

Add '2.332561986' to each side of the equation.
-3.054545455x + 2.332561986 + x2 = -0.2545454545 + 2.332561986

Reorder the terms:
2.332561986 + -3.054545455x + x2 = -0.2545454545 + 2.332561986

Combine like terms: -0.2545454545 + 2.332561986 = 2.0780165315
2.332561986 + -3.054545455x + x2 = 2.0780165315

Factor a perfect square on the left side:
(x + -1.527272728)(x + -1.527272728) = 2.0780165315

Calculate the square root of the right side: 1.441532702

Break this problem into two subproblems by setting 
(x + -1.527272728) equal to 1.441532702 and -1.441532702.

Subproblem 1
x + -1.527272728 = 1.441532702

Simplifying
x + -1.527272728 = 1.441532702

Reorder the terms:
-1.527272728 + x = 1.441532702

Solving
-1.527272728 + x = 1.441532702

Solving for variable 'x'.

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

Add '1.527272728' to each side of the equation.
-1.527272728 + 1.527272728 + x = 1.441532702 + 1.527272728

Combine like terms: -1.527272728 + 1.527272728 = 0.000000000
0.000000000 + x = 1.441532702 + 1.527272728
x = 1.441532702 + 1.527272728

Combine like terms: 1.441532702 + 1.527272728 = 2.96880543
x = 2.96880543

Simplifying
x = 2.96880543

Subproblem 2
x + -1.527272728 = -1.441532702

Simplifying
x + -1.527272728 = -1.441532702

Reorder the terms:
-1.527272728 + x = -1.441532702

Solving
-1.527272728 + x = -1.441532702

Solving for variable 'x'.

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

Add '1.527272728' to each side of the equation.
-1.527272728 + 1.527272728 + x = -1.441532702 + 1.527272728

Combine like terms: -1.527272728 + 1.527272728 = 0.000000000
0.000000000 + x = -1.441532702 + 1.527272728
x = -1.441532702 + 1.527272728

Combine like terms: -1.441532702 + 1.527272728 = 0.085740026
x = 0.085740026

Simplifying
x = 0.085740026

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.96880543, 0.085740026}
Solution
x = {2.96880543, 0.085740026}