x^2+0.5x+0.06=0

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Solution for x^2+0.5x+0.06=0 equation: 


Simplifying
x2 + 0.5x + 0.06 = 0

Reorder the terms:
0.06 + 0.5x + x2 = 0

Solving
0.06 + 0.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.06' to each side of the equation.
0.06 + 0.5x + -0.06 + x2 = 0 + -0.06

Reorder the terms:
0.06 + -0.06 + 0.5x + x2 = 0 + -0.06

Combine like terms: 0.06 + -0.06 = 0.00
0.00 + 0.5x + x2 = 0 + -0.06
0.5x + x2 = 0 + -0.06

Combine like terms: 0 + -0.06 = -0.06
0.5x + x2 = -0.06

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -0.06 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -0.06 + 0.0625

Combine like terms: -0.06 + 0.0625 = 0.0025
0.0625 + 0.5x + x2 = 0.0025

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.0025

Calculate the square root of the right side: 0.05

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.05 and -0.05.


Subproblem 1
x + 0.25 = 0.05

Simplifying
x + 0.25 = 0.05

Reorder the terms:
0.25 + x = 0.05

Solving
0.25 + x = 0.05

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.05 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.05 + -0.25
x = 0.05 + -0.25

Combine like terms: 0.05 + -0.25 = -0.2
x = -0.2

Simplifying
x = -0.2


Subproblem 2
x + 0.25 = -0.05

Simplifying
x + 0.25 = -0.05

Reorder the terms:
0.25 + x = -0.05

Solving
0.25 + x = -0.05

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.05 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.05 + -0.25
x = -0.05 + -0.25

Combine like terms: -0.05 + -0.25 = -0.3
x = -0.3

Simplifying
x = -0.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.2, -0.3}

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