x^2+2x+1=97834519873

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Solution for x^2+2x+1=97834519873 equation:


Simplifying
x2 + 2x + 1 = 97834519873

Reorder the terms:
1 + 2x + x2 = 97834519873

Solving
1 + 2x + x2 = 97834519873

Solving for variable 'x'.

Reorder the terms:
1 + -97834519873 + 2x + x2 = 97834519873 + -97834519873

Combine like terms: 1 + -97834519873 = -97834519872
-97834519872 + 2x + x2 = 97834519873 + -97834519873

Combine like terms: 97834519873 + -97834519873 = 0
-97834519872 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '97834519872' to each side of the equation.
-97834519872 + 2x + 97834519872 + x2 = 0 + 97834519872

Reorder the terms:
-97834519872 + 97834519872 + 2x + x2 = 0 + 97834519872

Combine like terms: -97834519872 + 97834519872 = 0
0 + 2x + x2 = 0 + 97834519872
2x + x2 = 0 + 97834519872

Combine like terms: 0 + 97834519872 = 97834519872
2x + x2 = 97834519872

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 97834519872 + 1

Reorder the terms:
1 + 2x + x2 = 97834519872 + 1

Combine like terms: 97834519872 + 1 = 97834519873
1 + 2x + x2 = 97834519873

Factor a perfect square on the left side:
(x + 1)(x + 1) = 97834519873

Calculate the square root of the right side: 312785.101743993

Break this problem into two subproblems by setting 
(x + 1) equal to 312785.101743993 and -312785.101743993.

Subproblem 1

x + 1 = 312785.101743993 Simplifying x + 1 = 312785.101743993 Reorder the terms: 1 + x = 312785.101743993 Solving 1 + x = 312785.101743993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 312785.101743993 + -1 Combine like terms: 1 + -1 = 0 0 + x = 312785.101743993 + -1 x = 312785.101743993 + -1 Combine like terms: 312785.101743993 + -1 = 312784.101743993 x = 312784.101743993 Simplifying x = 312784.101743993

Subproblem 2

x + 1 = -312785.101743993 Simplifying x + 1 = -312785.101743993 Reorder the terms: 1 + x = -312785.101743993 Solving 1 + x = -312785.101743993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -312785.101743993 + -1 Combine like terms: 1 + -1 = 0 0 + x = -312785.101743993 + -1 x = -312785.101743993 + -1 Combine like terms: -312785.101743993 + -1 = -312786.101743993 x = -312786.101743993 Simplifying x = -312786.101743993

Solution

The solution to the problem is based on the solutions from the subproblems. x = {312784.101743993, -312786.101743993}

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