100x+x^2=100+2x

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


Simplifying
100x + x2 = 100 + 2x

Solving
100x + x2 = 100 + 2x

Solving for variable 'x'.

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

Combine like terms: 100x + -2x = 98x
-100 + 98x + x2 = 100 + 2x + -100 + -2x

Reorder the terms:
-100 + 98x + x2 = 100 + -100 + 2x + -2x

Combine like terms: 100 + -100 = 0
-100 + 98x + x2 = 0 + 2x + -2x
-100 + 98x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-100 + 98x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 98x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 98x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 98x + x2 = 0 + 100
98x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
98x + x2 = 100

The x term is 98x.  Take half its coefficient (49).
Square it (2401) and add it to both sides.

Add '2401' to each side of the equation.
98x + 2401 + x2 = 100 + 2401

Reorder the terms:
2401 + 98x + x2 = 100 + 2401

Combine like terms: 100 + 2401 = 2501
2401 + 98x + x2 = 2501

Factor a perfect square on the left side:
(x + 49)(x + 49) = 2501

Calculate the square root of the right side: 50.009999

Break this problem into two subproblems by setting 
(x + 49) equal to 50.009999 and -50.009999.

Subproblem 1

x + 49 = 50.009999 Simplifying x + 49 = 50.009999 Reorder the terms: 49 + x = 50.009999 Solving 49 + x = 50.009999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-49' to each side of the equation. 49 + -49 + x = 50.009999 + -49 Combine like terms: 49 + -49 = 0 0 + x = 50.009999 + -49 x = 50.009999 + -49 Combine like terms: 50.009999 + -49 = 1.009999 x = 1.009999 Simplifying x = 1.009999

Subproblem 2

x + 49 = -50.009999 Simplifying x + 49 = -50.009999 Reorder the terms: 49 + x = -50.009999 Solving 49 + x = -50.009999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-49' to each side of the equation. 49 + -49 + x = -50.009999 + -49 Combine like terms: 49 + -49 = 0 0 + x = -50.009999 + -49 x = -50.009999 + -49 Combine like terms: -50.009999 + -49 = -99.009999 x = -99.009999 Simplifying x = -99.009999

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.009999, -99.009999}

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