x^2+x+.25=15.93945+.25

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Solution for x^2+x+.25=15.93945+.25 equation: 


Simplifying
x2 + x + 0.25 = 15.93945 + 0.25

Reorder the terms:
0.25 + x + x2 = 15.93945 + 0.25

Combine like terms: 15.93945 + 0.25 = 16.18945
0.25 + x + x2 = 16.18945

Solving
0.25 + x + x2 = 16.18945

Solving for variable 'x'.

Reorder the terms:
0.25 + -16.18945 + x + x2 = 16.18945 + -16.18945

Combine like terms: 0.25 + -16.18945 = -15.93945
-15.93945 + x + x2 = 16.18945 + -16.18945

Combine like terms: 16.18945 + -16.18945 = 0.00000
-15.93945 + x + x2 = 0.00000

Begin completing the square.

Move the constant term to the right:

Add '15.93945' to each side of the equation.
-15.93945 + x + 15.93945 + x2 = 0.00000 + 15.93945

Reorder the terms:
-15.93945 + 15.93945 + x + x2 = 0.00000 + 15.93945

Combine like terms: -15.93945 + 15.93945 = 0.00000
0.00000 + x + x2 = 0.00000 + 15.93945
x + x2 = 0.00000 + 15.93945

Combine like terms: 0.00000 + 15.93945 = 15.93945
x + x2 = 15.93945

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 15.93945 + 0.25

Reorder the terms:
0.25 + x + x2 = 15.93945 + 0.25

Combine like terms: 15.93945 + 0.25 = 16.18945
0.25 + x + x2 = 16.18945

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 16.18945

Calculate the square root of the right side: 4.023611562

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.023611562 and -4.023611562.


Subproblem 1
x + 0.5 = 4.023611562

Simplifying
x + 0.5 = 4.023611562

Reorder the terms:
0.5 + x = 4.023611562

Solving
0.5 + x = 4.023611562

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 4.023611562 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.023611562 + -0.5
x = 4.023611562 + -0.5

Combine like terms: 4.023611562 + -0.5 = 3.523611562
x = 3.523611562

Simplifying
x = 3.523611562


Subproblem 2
x + 0.5 = -4.023611562

Simplifying
x + 0.5 = -4.023611562

Reorder the terms:
0.5 + x = -4.023611562

Solving
0.5 + x = -4.023611562

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -4.023611562 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.023611562 + -0.5
x = -4.023611562 + -0.5

Combine like terms: -4.023611562 + -0.5 = -4.523611562
x = -4.523611562

Simplifying
x = -4.523611562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.523611562, -4.523611562}

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