x^2+0.0938*x-0.049=0

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Solution for x^2+0.0938*x-0.049=0 equation: 


Simplifying
x2 + 0.0938x + -0.049 = 0

Reorder the terms:
-0.049 + 0.0938x + x2 = 0

Solving
-0.049 + 0.0938x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.049' to each side of the equation.
-0.049 + 0.0938x + 0.049 + x2 = 0 + 0.049

Reorder the terms:
-0.049 + 0.049 + 0.0938x + x2 = 0 + 0.049

Combine like terms: -0.049 + 0.049 = 0.000
0.000 + 0.0938x + x2 = 0 + 0.049
0.0938x + x2 = 0 + 0.049

Combine like terms: 0 + 0.049 = 0.049
0.0938x + x2 = 0.049

The x term is 0.0938x.  Take half its coefficient (0.0469).
Square it (0.00219961) and add it to both sides.

Add '0.00219961' to each side of the equation.
0.0938x + 0.00219961 + x2 = 0.049 + 0.00219961

Reorder the terms:
0.00219961 + 0.0938x + x2 = 0.049 + 0.00219961

Combine like terms: 0.049 + 0.00219961 = 0.05119961
0.00219961 + 0.0938x + x2 = 0.05119961

Factor a perfect square on the left side:
(x + 0.0469)(x + 0.0469) = 0.05119961

Calculate the square root of the right side: 0.226273308

Break this problem into two subproblems by setting 
(x + 0.0469) equal to 0.226273308 and -0.226273308.


Subproblem 1
x + 0.0469 = 0.226273308

Simplifying
x + 0.0469 = 0.226273308

Reorder the terms:
0.0469 + x = 0.226273308

Solving
0.0469 + x = 0.226273308

Solving for variable 'x'.

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

Add '-0.0469' to each side of the equation.
0.0469 + -0.0469 + x = 0.226273308 + -0.0469

Combine like terms: 0.0469 + -0.0469 = 0.0000
0.0000 + x = 0.226273308 + -0.0469
x = 0.226273308 + -0.0469

Combine like terms: 0.226273308 + -0.0469 = 0.179373308
x = 0.179373308

Simplifying
x = 0.179373308


Subproblem 2
x + 0.0469 = -0.226273308

Simplifying
x + 0.0469 = -0.226273308

Reorder the terms:
0.0469 + x = -0.226273308

Solving
0.0469 + x = -0.226273308

Solving for variable 'x'.

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

Add '-0.0469' to each side of the equation.
0.0469 + -0.0469 + x = -0.226273308 + -0.0469

Combine like terms: 0.0469 + -0.0469 = 0.0000
0.0000 + x = -0.226273308 + -0.0469
x = -0.226273308 + -0.0469

Combine like terms: -0.226273308 + -0.0469 = -0.273173308
x = -0.273173308

Simplifying
x = -0.273173308


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.179373308, -0.273173308}

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