x^2-0.1x-0.035=0

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Solution for x^2-0.1x-0.035=0 equation: 


Simplifying
x2 + -0.1x + -0.035 = 0

Reorder the terms:
-0.035 + -0.1x + x2 = 0

Solving
-0.035 + -0.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.035' to each side of the equation.
-0.035 + -0.1x + 0.035 + x2 = 0 + 0.035

Reorder the terms:
-0.035 + 0.035 + -0.1x + x2 = 0 + 0.035

Combine like terms: -0.035 + 0.035 = 0.000
0.000 + -0.1x + x2 = 0 + 0.035
-0.1x + x2 = 0 + 0.035

Combine like terms: 0 + 0.035 = 0.035
-0.1x + x2 = 0.035

The x term is -0.1x.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1x + 0.0025 + x2 = 0.035 + 0.0025

Reorder the terms:
0.0025 + -0.1x + x2 = 0.035 + 0.0025

Combine like terms: 0.035 + 0.0025 = 0.0375
0.0025 + -0.1x + x2 = 0.0375

Factor a perfect square on the left side:
(x + -0.05)(x + -0.05) = 0.0375

Calculate the square root of the right side: 0.193649167

Break this problem into two subproblems by setting 
(x + -0.05) equal to 0.193649167 and -0.193649167.


Subproblem 1
x + -0.05 = 0.193649167

Simplifying
x + -0.05 = 0.193649167

Reorder the terms:
-0.05 + x = 0.193649167

Solving
-0.05 + x = 0.193649167

Solving for variable 'x'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + x = 0.193649167 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + x = 0.193649167 + 0.05
x = 0.193649167 + 0.05

Combine like terms: 0.193649167 + 0.05 = 0.243649167
x = 0.243649167

Simplifying
x = 0.243649167


Subproblem 2
x + -0.05 = -0.193649167

Simplifying
x + -0.05 = -0.193649167

Reorder the terms:
-0.05 + x = -0.193649167

Solving
-0.05 + x = -0.193649167

Solving for variable 'x'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + x = -0.193649167 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + x = -0.193649167 + 0.05
x = -0.193649167 + 0.05

Combine like terms: -0.193649167 + 0.05 = -0.143649167
x = -0.143649167

Simplifying
x = -0.143649167


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.243649167, -0.143649167}

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