x^2+x+0.25=6.35

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Solution for x^2+x+0.25=6.35 equation: 


Simplifying
x2 + x + 0.25 = 6.35

Reorder the terms:
0.25 + x + x2 = 6.35

Solving
0.25 + x + x2 = 6.35

Solving for variable 'x'.

Reorder the terms:
0.25 + -6.35 + x + x2 = 6.35 + -6.35

Combine like terms: 0.25 + -6.35 = -6.1
-6.1 + x + x2 = 6.35 + -6.35

Combine like terms: 6.35 + -6.35 = 0.00
-6.1 + x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '6.1' to each side of the equation.
-6.1 + x + 6.1 + x2 = 0.00 + 6.1

Reorder the terms:
-6.1 + 6.1 + x + x2 = 0.00 + 6.1

Combine like terms: -6.1 + 6.1 = 0.0
0.0 + x + x2 = 0.00 + 6.1
x + x2 = 0.00 + 6.1

Combine like terms: 0.00 + 6.1 = 6.1
x + x2 = 6.1

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 = 6.1 + 0.25

Reorder the terms:
0.25 + x + x2 = 6.1 + 0.25

Combine like terms: 6.1 + 0.25 = 6.35
0.25 + x + x2 = 6.35

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 6.35

Calculate the square root of the right side: 2.519920634

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.519920634 and -2.519920634.


Subproblem 1
x + 0.5 = 2.519920634

Simplifying
x + 0.5 = 2.519920634

Reorder the terms:
0.5 + x = 2.519920634

Solving
0.5 + x = 2.519920634

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 = 2.519920634 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.519920634 + -0.5
x = 2.519920634 + -0.5

Combine like terms: 2.519920634 + -0.5 = 2.019920634
x = 2.019920634

Simplifying
x = 2.019920634


Subproblem 2
x + 0.5 = -2.519920634

Simplifying
x + 0.5 = -2.519920634

Reorder the terms:
0.5 + x = -2.519920634

Solving
0.5 + x = -2.519920634

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 = -2.519920634 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.519920634 + -0.5
x = -2.519920634 + -0.5

Combine like terms: -2.519920634 + -0.5 = -3.019920634
x = -3.019920634

Simplifying
x = -3.019920634


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.019920634, -3.019920634}

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