(d+0.5)(d+0.5)=1

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Solution for (d+0.5)(d+0.5)=1 equation: 


Simplifying
(d + 0.5)(d + 0.5) = 1

Reorder the terms:
(0.5 + d)(d + 0.5) = 1

Reorder the terms:
(0.5 + d)(0.5 + d) = 1

Multiply (0.5 + d) * (0.5 + d)
(0.5(0.5 + d) + d(0.5 + d)) = 1
((0.5 * 0.5 + d * 0.5) + d(0.5 + d)) = 1
((0.25 + 0.5d) + d(0.5 + d)) = 1
(0.25 + 0.5d + (0.5 * d + d * d)) = 1
(0.25 + 0.5d + (0.5d + d2)) = 1

Combine like terms: 0.5d + 0.5d = 1d
(0.25 + 1d + d2) = 1

Solving
0.25 + 1d + d2 = 1

Solving for variable 'd'.

Reorder the terms:
0.25 + -1 + 1d + d2 = 1 + -1

Combine like terms: 0.25 + -1 = -0.75
-0.75 + 1d + d2 = 1 + -1

Combine like terms: 1 + -1 = 0
-0.75 + 1d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 1d + 0.75 + d2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 1d + d2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 1d + d2 = 0 + 0.75
1d + d2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
1d + d2 = 0.75

The d term is 1d.  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.
d + 0.25 + d2 = 0.75 + 0.25

Reorder the terms:
0.25 + d + d2 = 0.75 + 0.25

Combine like terms: 0.75 + 0.25 = 1
0.25 + d + d2 = 1

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

Calculate the square root of the right side: 1

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


Subproblem 1
d + 0.5 = 1

Simplifying
d + 0.5 = 1

Reorder the terms:
0.5 + d = 1

Solving
0.5 + d = 1

Solving for variable 'd'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + d = 1 + -0.5

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

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

Simplifying
d = 0.5


Subproblem 2
d + 0.5 = -1

Simplifying
d + 0.5 = -1

Reorder the terms:
0.5 + d = -1

Solving
0.5 + d = -1

Solving for variable 'd'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + d = -1 + -0.5

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

Combine like terms: -1 + -0.5 = -1.5
d = -1.5

Simplifying
d = -1.5


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

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