100+2x+0.0025x^2=1

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Solution for 100+2x+0.0025x^2=1 equation: 


Simplifying
100 + 2x + 0.0025x2 = 1

Solving
100 + 2x + 0.0025x2 = 1

Solving for variable 'x'.

Reorder the terms:
100 + -1 + 2x + 0.0025x2 = 1 + -1

Combine like terms: 100 + -1 = 99
99 + 2x + 0.0025x2 = 1 + -1

Combine like terms: 1 + -1 = 0
99 + 2x + 0.0025x2 = 0

Begin completing the square.  Divide all terms by
0.0025 the coefficient of the squared term: 

Divide each side by '0.0025'.
39600 + 800x + x2 = 0

Move the constant term to the right:

Add '-39600' to each side of the equation.
39600 + 800x + -39600 + x2 = 0 + -39600

Reorder the terms:
39600 + -39600 + 800x + x2 = 0 + -39600

Combine like terms: 39600 + -39600 = 0
0 + 800x + x2 = 0 + -39600
800x + x2 = 0 + -39600

Combine like terms: 0 + -39600 = -39600
800x + x2 = -39600

The x term is 800x.  Take half its coefficient (400).
Square it (160000) and add it to both sides.

Add '160000' to each side of the equation.
800x + 160000 + x2 = -39600 + 160000

Reorder the terms:
160000 + 800x + x2 = -39600 + 160000

Combine like terms: -39600 + 160000 = 120400
160000 + 800x + x2 = 120400

Factor a perfect square on the left side:
(x + 400)(x + 400) = 120400

Calculate the square root of the right side: 346.987031458

Break this problem into two subproblems by setting 
(x + 400) equal to 346.987031458 and -346.987031458.


Subproblem 1
x + 400 = 346.987031458

Simplifying
x + 400 = 346.987031458

Reorder the terms:
400 + x = 346.987031458

Solving
400 + x = 346.987031458

Solving for variable 'x'.

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

Add '-400' to each side of the equation.
400 + -400 + x = 346.987031458 + -400

Combine like terms: 400 + -400 = 0
0 + x = 346.987031458 + -400
x = 346.987031458 + -400

Combine like terms: 346.987031458 + -400 = -53.012968542
x = -53.012968542

Simplifying
x = -53.012968542


Subproblem 2
x + 400 = -346.987031458

Simplifying
x + 400 = -346.987031458

Reorder the terms:
400 + x = -346.987031458

Solving
400 + x = -346.987031458

Solving for variable 'x'.

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

Add '-400' to each side of the equation.
400 + -400 + x = -346.987031458 + -400

Combine like terms: 400 + -400 = 0
0 + x = -346.987031458 + -400
x = -346.987031458 + -400

Combine like terms: -346.987031458 + -400 = -746.987031458
x = -746.987031458

Simplifying
x = -746.987031458


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-53.012968542, -746.987031458}

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