x^2+0.011x=0.28

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Solution for x^2+0.011x=0.28 equation:


Simplifying
x2 + 0.011x = 0.28

Reorder the terms:
0.011x + x2 = 0.28

Solving
0.011x + x2 = 0.28

Solving for variable 'x'.

Reorder the terms:
-0.28 + 0.011x + x2 = 0.28 + -0.28

Combine like terms: 0.28 + -0.28 = 0.00
-0.28 + 0.011x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.28' to each side of the equation.
-0.28 + 0.011x + 0.28 + x2 = 0.00 + 0.28

Reorder the terms:
-0.28 + 0.28 + 0.011x + x2 = 0.00 + 0.28

Combine like terms: -0.28 + 0.28 = 0.00
0.00 + 0.011x + x2 = 0.00 + 0.28
0.011x + x2 = 0.00 + 0.28

Combine like terms: 0.00 + 0.28 = 0.28
0.011x + x2 = 0.28

The x term is 0.011x.  Take half its coefficient (0.0055).
Square it (0.00003025) and add it to both sides.

Add '0.00003025' to each side of the equation.
0.011x + 0.00003025 + x2 = 0.28 + 0.00003025

Reorder the terms:
0.00003025 + 0.011x + x2 = 0.28 + 0.00003025

Combine like terms: 0.28 + 0.00003025 = 0.28003025
0.00003025 + 0.011x + x2 = 0.28003025

Factor a perfect square on the left side:
(x + 0.0055)(x + 0.0055) = 0.28003025

Calculate the square root of the right side: 0.529178845

Break this problem into two subproblems by setting 
(x + 0.0055) equal to 0.529178845 and -0.529178845.


Subproblem 1
x + 0.0055 = 0.529178845

Simplifying
x + 0.0055 = 0.529178845

Reorder the terms:
0.0055 + x = 0.529178845

Solving
0.0055 + x = 0.529178845

Solving for variable 'x'.

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

Add '-0.0055' to each side of the equation.
0.0055 + -0.0055 + x = 0.529178845 + -0.0055

Combine like terms: 0.0055 + -0.0055 = 0.0000
0.0000 + x = 0.529178845 + -0.0055
x = 0.529178845 + -0.0055

Combine like terms: 0.529178845 + -0.0055 = 0.523678845
x = 0.523678845

Simplifying
x = 0.523678845


Subproblem 2
x + 0.0055 = -0.529178845

Simplifying
x + 0.0055 = -0.529178845

Reorder the terms:
0.0055 + x = -0.529178845

Solving
0.0055 + x = -0.529178845

Solving for variable 'x'.

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

Add '-0.0055' to each side of the equation.
0.0055 + -0.0055 + x = -0.529178845 + -0.0055

Combine like terms: 0.0055 + -0.0055 = 0.0000
0.0000 + x = -0.529178845 + -0.0055
x = -0.529178845 + -0.0055

Combine like terms: -0.529178845 + -0.0055 = -0.534678845
x = -0.534678845

Simplifying
x = -0.534678845


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.523678845, -0.534678845}

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