x^2+0.0477x-0.00028=0

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Solution for x^2+0.0477x-0.00028=0 equation:


Simplifying
x2 + 0.0477x + -0.00028 = 0

Reorder the terms:
-0.00028 + 0.0477x + x2 = 0

Solving
-0.00028 + 0.0477x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.00028' to each side of the equation.
-0.00028 + 0.0477x + 0.00028 + x2 = 0 + 0.00028

Reorder the terms:
-0.00028 + 0.00028 + 0.0477x + x2 = 0 + 0.00028

Combine like terms: -0.00028 + 0.00028 = 0.00000
0.00000 + 0.0477x + x2 = 0 + 0.00028
0.0477x + x2 = 0 + 0.00028

Combine like terms: 0 + 0.00028 = 0.00028
0.0477x + x2 = 0.00028

The x term is 0.0477x.  Take half its coefficient (0.02385).
Square it (0.0005688225) and add it to both sides.

Add '0.0005688225' to each side of the equation.
0.0477x + 0.0005688225 + x2 = 0.00028 + 0.0005688225

Reorder the terms:
0.0005688225 + 0.0477x + x2 = 0.00028 + 0.0005688225

Combine like terms: 0.00028 + 0.0005688225 = 0.0008488225
0.0005688225 + 0.0477x + x2 = 0.0008488225

Factor a perfect square on the left side:
(x + 0.02385)(x + 0.02385) = 0.0008488225

Calculate the square root of the right side: 0.029134559

Break this problem into two subproblems by setting 
(x + 0.02385) equal to 0.029134559 and -0.029134559.


Subproblem 1
x + 0.02385 = 0.029134559

Simplifying
x + 0.02385 = 0.029134559

Reorder the terms:
0.02385 + x = 0.029134559

Solving
0.02385 + x = 0.029134559

Solving for variable 'x'.

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

Add '-0.02385' to each side of the equation.
0.02385 + -0.02385 + x = 0.029134559 + -0.02385

Combine like terms: 0.02385 + -0.02385 = 0.00000
0.00000 + x = 0.029134559 + -0.02385
x = 0.029134559 + -0.02385

Combine like terms: 0.029134559 + -0.02385 = 0.005284559
x = 0.005284559

Simplifying
x = 0.005284559


Subproblem 2
x + 0.02385 = -0.029134559

Simplifying
x + 0.02385 = -0.029134559

Reorder the terms:
0.02385 + x = -0.029134559

Solving
0.02385 + x = -0.029134559

Solving for variable 'x'.

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

Add '-0.02385' to each side of the equation.
0.02385 + -0.02385 + x = -0.029134559 + -0.02385

Combine like terms: 0.02385 + -0.02385 = 0.00000
0.00000 + x = -0.029134559 + -0.02385
x = -0.029134559 + -0.02385

Combine like terms: -0.029134559 + -0.02385 = -0.052984559
x = -0.052984559

Simplifying
x = -0.052984559


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.005284559, -0.052984559}

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