0.01x^2-2x+1=0

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Solution for 0.01x^2-2x+1=0 equation:


Simplifying
0.01x2 + -2x + 1 = 0

Reorder the terms:
1 + -2x + 0.01x2 = 0

Solving
1 + -2x + 0.01x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.01'.
100 + -200x + x2 = 0

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -200x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + -200x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -200x + x2 = 0 + -100
-200x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
-200x + x2 = -100

The x term is -200x.  Take half its coefficient (-100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
-200x + 10000 + x2 = -100 + 10000

Reorder the terms:
10000 + -200x + x2 = -100 + 10000

Combine like terms: -100 + 10000 = 9900
10000 + -200x + x2 = 9900

Factor a perfect square on the left side:
(x + -100)(x + -100) = 9900

Calculate the square root of the right side: 99.498743711

Break this problem into two subproblems by setting 
(x + -100) equal to 99.498743711 and -99.498743711.

Subproblem 1

x + -100 = 99.498743711 Simplifying x + -100 = 99.498743711 Reorder the terms: -100 + x = 99.498743711 Solving -100 + x = 99.498743711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 99.498743711 + 100 Combine like terms: -100 + 100 = 0 0 + x = 99.498743711 + 100 x = 99.498743711 + 100 Combine like terms: 99.498743711 + 100 = 199.498743711 x = 199.498743711 Simplifying x = 199.498743711

Subproblem 2

x + -100 = -99.498743711 Simplifying x + -100 = -99.498743711 Reorder the terms: -100 + x = -99.498743711 Solving -100 + x = -99.498743711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -99.498743711 + 100 Combine like terms: -100 + 100 = 0 0 + x = -99.498743711 + 100 x = -99.498743711 + 100 Combine like terms: -99.498743711 + 100 = 0.501256289 x = 0.501256289 Simplifying x = 0.501256289

Solution

The solution to the problem is based on the solutions from the subproblems. x = {199.498743711, 0.501256289}

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