(x-.5)(x-.5)=1.5

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Solution for (x-.5)(x-.5)=1.5 equation: 


Simplifying
(x + -0.5)(x + -0.5) = 1.5

Reorder the terms:
(-0.5 + x)(x + -0.5) = 1.5

Reorder the terms:
(-0.5 + x)(-0.5 + x) = 1.5

Multiply (-0.5 + x) * (-0.5 + x)
(-0.5(-0.5 + x) + x(-0.5 + x)) = 1.5
((-0.5 * -0.5 + x * -0.5) + x(-0.5 + x)) = 1.5
((0.25 + -0.5x) + x(-0.5 + x)) = 1.5
(0.25 + -0.5x + (-0.5 * x + x * x)) = 1.5
(0.25 + -0.5x + (-0.5x + x2)) = 1.5

Combine like terms: -0.5x + -0.5x = -1x
(0.25 + -1x + x2) = 1.5

Solving
0.25 + -1x + x2 = 1.5

Solving for variable 'x'.

Reorder the terms:
0.25 + -1.5 + -1x + x2 = 1.5 + -1.5

Combine like terms: 0.25 + -1.5 = -1.25
-1.25 + -1x + x2 = 1.5 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
-1.25 + -1x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1x + 1.25 + x2 = 0.0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1x + x2 = 0.0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1x + x2 = 0.0 + 1.25
-1x + x2 = 0.0 + 1.25

Combine like terms: 0.0 + 1.25 = 1.25
-1x + x2 = 1.25

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 = 1.25 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.25 + 0.25

Combine like terms: 1.25 + 0.25 = 1.5
0.25 + -1x + x2 = 1.5

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.224744871 and -1.224744871.


Subproblem 1
x + -0.5 = 1.224744871

Simplifying
x + -0.5 = 1.224744871

Reorder the terms:
-0.5 + x = 1.224744871

Solving
-0.5 + x = 1.224744871

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 = 1.224744871 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.224744871 + 0.5
x = 1.224744871 + 0.5

Combine like terms: 1.224744871 + 0.5 = 1.724744871
x = 1.724744871

Simplifying
x = 1.724744871


Subproblem 2
x + -0.5 = -1.224744871

Simplifying
x + -0.5 = -1.224744871

Reorder the terms:
-0.5 + x = -1.224744871

Solving
-0.5 + x = -1.224744871

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 = -1.224744871 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.224744871 + 0.5
x = -1.224744871 + 0.5

Combine like terms: -1.224744871 + 0.5 = -0.724744871
x = -0.724744871

Simplifying
x = -0.724744871


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.724744871, -0.724744871}

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