x^2+x+0.25=49

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Solution for x^2+x+0.25=49 equation: 


Simplifying
x2 + x + 0.25 = 49

Reorder the terms:
0.25 + x + x2 = 49

Solving
0.25 + x + x2 = 49

Solving for variable 'x'.

Reorder the terms:
0.25 + -49 + x + x2 = 49 + -49

Combine like terms: 0.25 + -49 = -48.75
-48.75 + x + x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-48.75 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48.75' to each side of the equation.
-48.75 + x + 48.75 + x2 = 0 + 48.75

Reorder the terms:
-48.75 + 48.75 + x + x2 = 0 + 48.75

Combine like terms: -48.75 + 48.75 = 0.00
0.00 + x + x2 = 0 + 48.75
x + x2 = 0 + 48.75

Combine like terms: 0 + 48.75 = 48.75
x + x2 = 48.75

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 = 48.75 + 0.25

Reorder the terms:
0.25 + x + x2 = 48.75 + 0.25

Combine like terms: 48.75 + 0.25 = 49
0.25 + x + x2 = 49

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 49

Calculate the square root of the right side: 7

Break this problem into two subproblems by setting 
(x + 0.5) equal to 7 and -7.


Subproblem 1
x + 0.5 = 7

Simplifying
x + 0.5 = 7

Reorder the terms:
0.5 + x = 7

Solving
0.5 + x = 7

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 = 7 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 7 + -0.5
x = 7 + -0.5

Combine like terms: 7 + -0.5 = 6.5
x = 6.5

Simplifying
x = 6.5


Subproblem 2
x + 0.5 = -7

Simplifying
x + 0.5 = -7

Reorder the terms:
0.5 + x = -7

Solving
0.5 + x = -7

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 = -7 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -7 + -0.5
x = -7 + -0.5

Combine like terms: -7 + -0.5 = -7.5
x = -7.5

Simplifying
x = -7.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.5, -7.5}

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