x^2+0.27x+0.01=0.1

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Solution for x^2+0.27x+0.01=0.1 equation: 


Simplifying
x2 + 0.27x + 0.01 = 0.1

Reorder the terms:
0.01 + 0.27x + x2 = 0.1

Solving
0.01 + 0.27x + x2 = 0.1

Solving for variable 'x'.

Reorder the terms:
0.01 + -0.1 + 0.27x + x2 = 0.1 + -0.1

Combine like terms: 0.01 + -0.1 = -0.09
-0.09 + 0.27x + x2 = 0.1 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
-0.09 + 0.27x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '0.09' to each side of the equation.
-0.09 + 0.27x + 0.09 + x2 = 0.0 + 0.09

Reorder the terms:
-0.09 + 0.09 + 0.27x + x2 = 0.0 + 0.09

Combine like terms: -0.09 + 0.09 = 0.00
0.00 + 0.27x + x2 = 0.0 + 0.09
0.27x + x2 = 0.0 + 0.09

Combine like terms: 0.0 + 0.09 = 0.09
0.27x + x2 = 0.09

The x term is 0.27x.  Take half its coefficient (0.135).
Square it (0.018225) and add it to both sides.

Add '0.018225' to each side of the equation.
0.27x + 0.018225 + x2 = 0.09 + 0.018225

Reorder the terms:
0.018225 + 0.27x + x2 = 0.09 + 0.018225

Combine like terms: 0.09 + 0.018225 = 0.108225
0.018225 + 0.27x + x2 = 0.108225

Factor a perfect square on the left side:
(x + 0.135)(x + 0.135) = 0.108225

Calculate the square root of the right side: 0.328975683

Break this problem into two subproblems by setting 
(x + 0.135) equal to 0.328975683 and -0.328975683.


Subproblem 1
x + 0.135 = 0.328975683

Simplifying
x + 0.135 = 0.328975683

Reorder the terms:
0.135 + x = 0.328975683

Solving
0.135 + x = 0.328975683

Solving for variable 'x'.

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

Add '-0.135' to each side of the equation.
0.135 + -0.135 + x = 0.328975683 + -0.135

Combine like terms: 0.135 + -0.135 = 0.000
0.000 + x = 0.328975683 + -0.135
x = 0.328975683 + -0.135

Combine like terms: 0.328975683 + -0.135 = 0.193975683
x = 0.193975683

Simplifying
x = 0.193975683


Subproblem 2
x + 0.135 = -0.328975683

Simplifying
x + 0.135 = -0.328975683

Reorder the terms:
0.135 + x = -0.328975683

Solving
0.135 + x = -0.328975683

Solving for variable 'x'.

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

Add '-0.135' to each side of the equation.
0.135 + -0.135 + x = -0.328975683 + -0.135

Combine like terms: 0.135 + -0.135 = 0.000
0.000 + x = -0.328975683 + -0.135
x = -0.328975683 + -0.135

Combine like terms: -0.328975683 + -0.135 = -0.463975683
x = -0.463975683

Simplifying
x = -0.463975683


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.193975683, -0.463975683}

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