100x^2+10001x+10=0

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Solution for 100x^2+10001x+10=0 equation:


Simplifying
100x2 + 10001x + 10 = 0

Reorder the terms:
10 + 10001x + 100x2 = 0

Solving
10 + 10001x + 100x2 = 0

Solving for variable 'x'.

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

Divide each side by '100'.
0.1 + 100.01x + x2 = 0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + 100.01x + -0.1 + x2 = 0 + -0.1

Reorder the terms:
0.1 + -0.1 + 100.01x + x2 = 0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + 100.01x + x2 = 0 + -0.1
100.01x + x2 = 0 + -0.1

Combine like terms: 0 + -0.1 = -0.1
100.01x + x2 = -0.1

The x term is 100.01x.  Take half its coefficient (50.005).
Square it (2500.500025) and add it to both sides.

Add '2500.500025' to each side of the equation.
100.01x + 2500.500025 + x2 = -0.1 + 2500.500025

Reorder the terms:
2500.500025 + 100.01x + x2 = -0.1 + 2500.500025

Combine like terms: -0.1 + 2500.500025 = 2500.400025
2500.500025 + 100.01x + x2 = 2500.400025

Factor a perfect square on the left side:
(x + 50.005)(x + 50.005) = 2500.400025

Calculate the square root of the right side: 50.00400009

Break this problem into two subproblems by setting 
(x + 50.005) equal to 50.00400009 and -50.00400009.

Subproblem 1

x + 50.005 = 50.00400009 Simplifying x + 50.005 = 50.00400009 Reorder the terms: 50.005 + x = 50.00400009 Solving 50.005 + x = 50.00400009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.005' to each side of the equation. 50.005 + -50.005 + x = 50.00400009 + -50.005 Combine like terms: 50.005 + -50.005 = 0.000 0.000 + x = 50.00400009 + -50.005 x = 50.00400009 + -50.005 Combine like terms: 50.00400009 + -50.005 = -0.00099991 x = -0.00099991 Simplifying x = -0.00099991

Subproblem 2

x + 50.005 = -50.00400009 Simplifying x + 50.005 = -50.00400009 Reorder the terms: 50.005 + x = -50.00400009 Solving 50.005 + x = -50.00400009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.005' to each side of the equation. 50.005 + -50.005 + x = -50.00400009 + -50.005 Combine like terms: 50.005 + -50.005 = 0.000 0.000 + x = -50.00400009 + -50.005 x = -50.00400009 + -50.005 Combine like terms: -50.00400009 + -50.005 = -100.00900009 x = -100.00900009 Simplifying x = -100.00900009

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.00099991, -100.00900009}

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