x^2-2x-43=-5x+1

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Solution for x^2-2x-43=-5x+1 equation: 


Simplifying
x2 + -2x + -43 = -5x + 1

Reorder the terms:
-43 + -2x + x2 = -5x + 1

Reorder the terms:
-43 + -2x + x2 = 1 + -5x

Solving
-43 + -2x + x2 = 1 + -5x

Solving for variable 'x'.

Reorder the terms:
-43 + -1 + -2x + 5x + x2 = 1 + -5x + -1 + 5x

Combine like terms: -43 + -1 = -44
-44 + -2x + 5x + x2 = 1 + -5x + -1 + 5x

Combine like terms: -2x + 5x = 3x
-44 + 3x + x2 = 1 + -5x + -1 + 5x

Reorder the terms:
-44 + 3x + x2 = 1 + -1 + -5x + 5x

Combine like terms: 1 + -1 = 0
-44 + 3x + x2 = 0 + -5x + 5x
-44 + 3x + x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-44 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 3x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + 3x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + 3x + x2 = 0 + 44
3x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
3x + x2 = 44

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 44 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 44 + 2.25

Combine like terms: 44 + 2.25 = 46.25
2.25 + 3x + x2 = 46.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
x + 1.5 = 6.800735254

Simplifying
x + 1.5 = 6.800735254

Reorder the terms:
1.5 + x = 6.800735254

Solving
1.5 + x = 6.800735254

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 6.800735254 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 6.800735254 + -1.5
x = 6.800735254 + -1.5

Combine like terms: 6.800735254 + -1.5 = 5.300735254
x = 5.300735254

Simplifying
x = 5.300735254


Subproblem 2
x + 1.5 = -6.800735254

Simplifying
x + 1.5 = -6.800735254

Reorder the terms:
1.5 + x = -6.800735254

Solving
1.5 + x = -6.800735254

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -6.800735254 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -6.800735254 + -1.5
x = -6.800735254 + -1.5

Combine like terms: -6.800735254 + -1.5 = -8.300735254
x = -8.300735254

Simplifying
x = -8.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.300735254, -8.300735254}

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