x^2-x+.25=1

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Solution for x^2-x+.25=1 equation: 


Simplifying
x2 + -1x + 0.25 = 1

Reorder the terms:
0.25 + -1x + x2 = 1

Solving
0.25 + -1x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
0.25 + -1 + -1x + x2 = 1 + -1

Combine like terms: 0.25 + -1 = -0.75
-0.75 + -1x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-0.75 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -1x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -1x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -1x + x2 = 0 + 0.75
-1x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-1x + x2 = 0.75

The x term is -1x.  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.
-1x + 0.25 + x2 = 0.75 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.75 + 0.25

Combine like terms: 0.75 + 0.25 = 1
0.25 + -1x + x2 = 1

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1 and -1.


Subproblem 1
x + -0.5 = 1

Simplifying
x + -0.5 = 1

Reorder the terms:
-0.5 + x = 1

Solving
-0.5 + x = 1

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 = 1 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1 + 0.5
x = 1 + 0.5

Combine like terms: 1 + 0.5 = 1.5
x = 1.5

Simplifying
x = 1.5


Subproblem 2
x + -0.5 = -1

Simplifying
x + -0.5 = -1

Reorder the terms:
-0.5 + x = -1

Solving
-0.5 + x = -1

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 = -1 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1 + 0.5
x = -1 + 0.5

Combine like terms: -1 + 0.5 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, -0.5}

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