X^2+0.036X+0.0001309=0

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Solution for X^2+0.036X+0.0001309=0 equation:


Simplifying
X2 + 0.036X + 0.0001309 = 0

Reorder the terms:
0.0001309 + 0.036X + X2 = 0

Solving
0.0001309 + 0.036X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-0.0001309' to each side of the equation.
0.0001309 + 0.036X + -0.0001309 + X2 = 0 + -0.0001309

Reorder the terms:
0.0001309 + -0.0001309 + 0.036X + X2 = 0 + -0.0001309

Combine like terms: 0.0001309 + -0.0001309 = 0.0000000
0.0000000 + 0.036X + X2 = 0 + -0.0001309
0.036X + X2 = 0 + -0.0001309

Combine like terms: 0 + -0.0001309 = -0.0001309
0.036X + X2 = -0.0001309

The X term is 0.036X.  Take half its coefficient (0.018).
Square it (0.000324) and add it to both sides.

Add '0.000324' to each side of the equation.
0.036X + 0.000324 + X2 = -0.0001309 + 0.000324

Reorder the terms:
0.000324 + 0.036X + X2 = -0.0001309 + 0.000324

Combine like terms: -0.0001309 + 0.000324 = 0.0001931
0.000324 + 0.036X + X2 = 0.0001931

Factor a perfect square on the left side:
(X + 0.018)(X + 0.018) = 0.0001931

Calculate the square root of the right side: 0.013896043

Break this problem into two subproblems by setting 
(X + 0.018) equal to 0.013896043 and -0.013896043.


Subproblem 1
X + 0.018 = 0.013896043

Simplifying
X + 0.018 = 0.013896043

Reorder the terms:
0.018 + X = 0.013896043

Solving
0.018 + X = 0.013896043

Solving for variable 'X'.

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

Add '-0.018' to each side of the equation.
0.018 + -0.018 + X = 0.013896043 + -0.018

Combine like terms: 0.018 + -0.018 = 0.000
0.000 + X = 0.013896043 + -0.018
X = 0.013896043 + -0.018

Combine like terms: 0.013896043 + -0.018 = -0.004103957
X = -0.004103957

Simplifying
X = -0.004103957


Subproblem 2
X + 0.018 = -0.013896043

Simplifying
X + 0.018 = -0.013896043

Reorder the terms:
0.018 + X = -0.013896043

Solving
0.018 + X = -0.013896043

Solving for variable 'X'.

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

Add '-0.018' to each side of the equation.
0.018 + -0.018 + X = -0.013896043 + -0.018

Combine like terms: 0.018 + -0.018 = 0.000
0.000 + X = -0.013896043 + -0.018
X = -0.013896043 + -0.018

Combine like terms: -0.013896043 + -0.018 = -0.031896043
X = -0.031896043

Simplifying
X = -0.031896043


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-0.004103957, -0.031896043}

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