x^2+0.9x+0.14=0

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Solution for x^2+0.9x+0.14=0 equation: 


Simplifying
x2 + 0.9x + 0.14 = 0

Reorder the terms:
0.14 + 0.9x + x2 = 0

Solving
0.14 + 0.9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.14' to each side of the equation.
0.14 + 0.9x + -0.14 + x2 = 0 + -0.14

Reorder the terms:
0.14 + -0.14 + 0.9x + x2 = 0 + -0.14

Combine like terms: 0.14 + -0.14 = 0.00
0.00 + 0.9x + x2 = 0 + -0.14
0.9x + x2 = 0 + -0.14

Combine like terms: 0 + -0.14 = -0.14
0.9x + x2 = -0.14

The x term is 0.9x.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9x + 0.2025 + x2 = -0.14 + 0.2025

Reorder the terms:
0.2025 + 0.9x + x2 = -0.14 + 0.2025

Combine like terms: -0.14 + 0.2025 = 0.0625
0.2025 + 0.9x + x2 = 0.0625

Factor a perfect square on the left side:
(x + 0.45)(x + 0.45) = 0.0625

Calculate the square root of the right side: 0.25

Break this problem into two subproblems by setting 
(x + 0.45) equal to 0.25 and -0.25.


Subproblem 1
x + 0.45 = 0.25

Simplifying
x + 0.45 = 0.25

Reorder the terms:
0.45 + x = 0.25

Solving
0.45 + x = 0.25

Solving for variable 'x'.

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

Add '-0.45' to each side of the equation.
0.45 + -0.45 + x = 0.25 + -0.45

Combine like terms: 0.45 + -0.45 = 0.00
0.00 + x = 0.25 + -0.45
x = 0.25 + -0.45

Combine like terms: 0.25 + -0.45 = -0.2
x = -0.2

Simplifying
x = -0.2


Subproblem 2
x + 0.45 = -0.25

Simplifying
x + 0.45 = -0.25

Reorder the terms:
0.45 + x = -0.25

Solving
0.45 + x = -0.25

Solving for variable 'x'.

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

Add '-0.45' to each side of the equation.
0.45 + -0.45 + x = -0.25 + -0.45

Combine like terms: 0.45 + -0.45 = 0.00
0.00 + x = -0.25 + -0.45
x = -0.25 + -0.45

Combine like terms: -0.25 + -0.45 = -0.7
x = -0.7

Simplifying
x = -0.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.2, -0.7}

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