x^2+0.38x-0.08=0

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Solution for x^2+0.38x-0.08=0 equation: 


Simplifying
x2 + 0.38x + -0.08 = 0

Reorder the terms:
-0.08 + 0.38x + x2 = 0

Solving
-0.08 + 0.38x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.08' to each side of the equation.
-0.08 + 0.38x + 0.08 + x2 = 0 + 0.08

Reorder the terms:
-0.08 + 0.08 + 0.38x + x2 = 0 + 0.08

Combine like terms: -0.08 + 0.08 = 0.00
0.00 + 0.38x + x2 = 0 + 0.08
0.38x + x2 = 0 + 0.08

Combine like terms: 0 + 0.08 = 0.08
0.38x + x2 = 0.08

The x term is 0.38x.  Take half its coefficient (0.19).
Square it (0.0361) and add it to both sides.

Add '0.0361' to each side of the equation.
0.38x + 0.0361 + x2 = 0.08 + 0.0361

Reorder the terms:
0.0361 + 0.38x + x2 = 0.08 + 0.0361

Combine like terms: 0.08 + 0.0361 = 0.1161
0.0361 + 0.38x + x2 = 0.1161

Factor a perfect square on the left side:
(x + 0.19)(x + 0.19) = 0.1161

Calculate the square root of the right side: 0.340734501

Break this problem into two subproblems by setting 
(x + 0.19) equal to 0.340734501 and -0.340734501.


Subproblem 1
x + 0.19 = 0.340734501

Simplifying
x + 0.19 = 0.340734501

Reorder the terms:
0.19 + x = 0.340734501

Solving
0.19 + x = 0.340734501

Solving for variable 'x'.

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

Add '-0.19' to each side of the equation.
0.19 + -0.19 + x = 0.340734501 + -0.19

Combine like terms: 0.19 + -0.19 = 0.00
0.00 + x = 0.340734501 + -0.19
x = 0.340734501 + -0.19

Combine like terms: 0.340734501 + -0.19 = 0.150734501
x = 0.150734501

Simplifying
x = 0.150734501


Subproblem 2
x + 0.19 = -0.340734501

Simplifying
x + 0.19 = -0.340734501

Reorder the terms:
0.19 + x = -0.340734501

Solving
0.19 + x = -0.340734501

Solving for variable 'x'.

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

Add '-0.19' to each side of the equation.
0.19 + -0.19 + x = -0.340734501 + -0.19

Combine like terms: 0.19 + -0.19 = 0.00
0.00 + x = -0.340734501 + -0.19
x = -0.340734501 + -0.19

Combine like terms: -0.340734501 + -0.19 = -0.530734501
x = -0.530734501

Simplifying
x = -0.530734501


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.150734501, -0.530734501}

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