0.0001+0.01*0.01x+x^2=1

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Solution for 0.0001+0.01*0.01x+x^2=1 equation:


Simplifying
0.0001 + 0.01 * 0.01x + x2 = 1

Multiply 0.01 * 0.01
0.0001 + 0.0001x + x2 = 1

Solving
0.0001 + 0.0001x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
0.0001 + -1 + 0.0001x + x2 = 1 + -1

Combine like terms: 0.0001 + -1 = -0.9999
-0.9999 + 0.0001x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-0.9999 + 0.0001x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.9999' to each side of the equation.
-0.9999 + 0.0001x + 0.9999 + x2 = 0 + 0.9999

Reorder the terms:
-0.9999 + 0.9999 + 0.0001x + x2 = 0 + 0.9999

Combine like terms: -0.9999 + 0.9999 = 0.0000
0.0000 + 0.0001x + x2 = 0 + 0.9999
0.0001x + x2 = 0 + 0.9999

Combine like terms: 0 + 0.9999 = 0.9999
0.0001x + x2 = 0.9999

The x term is 0.0001x.  Take half its coefficient (0.00005).
Square it (0.0000000025) and add it to both sides.

Add '0.0000000025' to each side of the equation.
0.0001x + 0.0000000025 + x2 = 0.9999 + 0.0000000025

Reorder the terms:
0.0000000025 + 0.0001x + x2 = 0.9999 + 0.0000000025

Combine like terms: 0.9999 + 0.0000000025 = 0.9999000025
0.0000000025 + 0.0001x + x2 = 0.9999000025

Factor a perfect square on the left side:
(x + 0.00005)(x + 0.00005) = 0.9999000025

Calculate the square root of the right side: 0.99995

Break this problem into two subproblems by setting 
(x + 0.00005) equal to 0.99995 and -0.99995.

Subproblem 1

x + 0.00005 = 0.99995 Simplifying x + 0.00005 = 0.99995 Reorder the terms: 0.00005 + x = 0.99995 Solving 0.00005 + x = 0.99995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00005' to each side of the equation. 0.00005 + -0.00005 + x = 0.99995 + -0.00005 Combine like terms: 0.00005 + -0.00005 = 0.00000 0.00000 + x = 0.99995 + -0.00005 x = 0.99995 + -0.00005 Combine like terms: 0.99995 + -0.00005 = 0.9999 x = 0.9999 Simplifying x = 0.9999

Subproblem 2

x + 0.00005 = -0.99995 Simplifying x + 0.00005 = -0.99995 Reorder the terms: 0.00005 + x = -0.99995 Solving 0.00005 + x = -0.99995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00005' to each side of the equation. 0.00005 + -0.00005 + x = -0.99995 + -0.00005 Combine like terms: 0.00005 + -0.00005 = 0.00000 0.00000 + x = -0.99995 + -0.00005 x = -0.99995 + -0.00005 Combine like terms: -0.99995 + -0.00005 = -1 x = -1 Simplifying x = -1

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9999, -1}

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