(x+0.4166666667)(x+0.4166666667)=0.4930555556

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Solution for (x+0.4166666667)(x+0.4166666667)=0.4930555556 equation: 


Simplifying
(x + 0.4166666667)(x + 0.4166666667) = 0.4930555556

Reorder the terms:
(0.4166666667 + x)(x + 0.4166666667) = 0.4930555556

Reorder the terms:
(0.4166666667 + x)(0.4166666667 + x) = 0.4930555556

Multiply (0.4166666667 + x) * (0.4166666667 + x)
(0.4166666667(0.4166666667 + x) + x(0.4166666667 + x)) = 0.4930555556
((0.4166666667 * 0.4166666667 + x * 0.4166666667) + x(0.4166666667 + x)) = 0.4930555556
((0.1736111111 + 0.4166666667x) + x(0.4166666667 + x)) = 0.4930555556
(0.1736111111 + 0.4166666667x + (0.4166666667 * x + x * x)) = 0.4930555556
(0.1736111111 + 0.4166666667x + (0.4166666667x + x2)) = 0.4930555556

Combine like terms: 0.4166666667x + 0.4166666667x = 0.8333333334x
(0.1736111111 + 0.8333333334x + x2) = 0.4930555556

Solving
0.1736111111 + 0.8333333334x + x2 = 0.4930555556

Solving for variable 'x'.

Reorder the terms:
0.1736111111 + -0.4930555556 + 0.8333333334x + x2 = 0.4930555556 + -0.4930555556

Combine like terms: 0.1736111111 + -0.4930555556 = -0.3194444445
-0.3194444445 + 0.8333333334x + x2 = 0.4930555556 + -0.4930555556

Combine like terms: 0.4930555556 + -0.4930555556 = 0.0000000000
-0.3194444445 + 0.8333333334x + x2 = 0.0000000000

Begin completing the square.

Move the constant term to the right:

Add '0.3194444445' to each side of the equation.
-0.3194444445 + 0.8333333334x + 0.3194444445 + x2 = 0.0000000000 + 0.3194444445

Reorder the terms:
-0.3194444445 + 0.3194444445 + 0.8333333334x + x2 = 0.0000000000 + 0.3194444445

Combine like terms: -0.3194444445 + 0.3194444445 = 0.0000000000
0.0000000000 + 0.8333333334x + x2 = 0.0000000000 + 0.3194444445
0.8333333334x + x2 = 0.0000000000 + 0.3194444445

Combine like terms: 0.0000000000 + 0.3194444445 = 0.3194444445
0.8333333334x + x2 = 0.3194444445

The x term is 0.8333333334x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333334x + 0.1736111111 + x2 = 0.3194444445 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333334x + x2 = 0.3194444445 + 0.1736111111

Combine like terms: 0.3194444445 + 0.1736111111 = 0.4930555556
0.1736111111 + 0.8333333334x + x2 = 0.4930555556

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = 0.4930555556

Calculate the square root of the right side: 0.702179148

Break this problem into two subproblems by setting 
(x + 0.4166666667) equal to 0.702179148 and -0.702179148.


Subproblem 1
x + 0.4166666667 = 0.702179148

Simplifying
x + 0.4166666667 = 0.702179148

Reorder the terms:
0.4166666667 + x = 0.702179148

Solving
0.4166666667 + x = 0.702179148

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = 0.702179148 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = 0.702179148 + -0.4166666667
x = 0.702179148 + -0.4166666667

Combine like terms: 0.702179148 + -0.4166666667 = 0.2855124813
x = 0.2855124813

Simplifying
x = 0.2855124813


Subproblem 2
x + 0.4166666667 = -0.702179148

Simplifying
x + 0.4166666667 = -0.702179148

Reorder the terms:
0.4166666667 + x = -0.702179148

Solving
0.4166666667 + x = -0.702179148

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = -0.702179148 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = -0.702179148 + -0.4166666667
x = -0.702179148 + -0.4166666667

Combine like terms: -0.702179148 + -0.4166666667 = -1.1188458147
x = -1.1188458147

Simplifying
x = -1.1188458147


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2855124813, -1.1188458147}

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