x^2-3x+x-3=5x-5

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Solution for x^2-3x+x-3=5x-5 equation: 


Simplifying
x2 + -3x + x + -3 = 5x + -5

Reorder the terms:
-3 + -3x + x + x2 = 5x + -5

Combine like terms: -3x + x = -2x
-3 + -2x + x2 = 5x + -5

Reorder the terms:
-3 + -2x + x2 = -5 + 5x

Solving
-3 + -2x + x2 = -5 + 5x

Solving for variable 'x'.

Reorder the terms:
-3 + 5 + -2x + -5x + x2 = -5 + 5x + 5 + -5x

Combine like terms: -3 + 5 = 2
2 + -2x + -5x + x2 = -5 + 5x + 5 + -5x

Combine like terms: -2x + -5x = -7x
2 + -7x + x2 = -5 + 5x + 5 + -5x

Reorder the terms:
2 + -7x + x2 = -5 + 5 + 5x + -5x

Combine like terms: -5 + 5 = 0
2 + -7x + x2 = 0 + 5x + -5x
2 + -7x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
2 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -7x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -7x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x + x2 = 0 + -2
-7x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-7x + x2 = -2

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -2 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -2 + 12.25

Combine like terms: -2 + 12.25 = 10.25
12.25 + -7x + x2 = 10.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + -3.5 = 3.201562119

Simplifying
x + -3.5 = 3.201562119

Reorder the terms:
-3.5 + x = 3.201562119

Solving
-3.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 3.201562119 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.201562119 + 3.5
x = 3.201562119 + 3.5

Combine like terms: 3.201562119 + 3.5 = 6.701562119
x = 6.701562119

Simplifying
x = 6.701562119


Subproblem 2
x + -3.5 = -3.201562119

Simplifying
x + -3.5 = -3.201562119

Reorder the terms:
-3.5 + x = -3.201562119

Solving
-3.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -3.201562119 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.201562119 + 3.5
x = -3.201562119 + 3.5

Combine like terms: -3.201562119 + 3.5 = 0.298437881
x = 0.298437881

Simplifying
x = 0.298437881


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.701562119, 0.298437881}

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