(x+0.5)(x+0.5)=15.75

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Solution for (x+0.5)(x+0.5)=15.75 equation: 


Simplifying
(x + 0.5)(x + 0.5) = 15.75

Reorder the terms:
(0.5 + x)(x + 0.5) = 15.75

Reorder the terms:
(0.5 + x)(0.5 + x) = 15.75

Multiply (0.5 + x) * (0.5 + x)
(0.5(0.5 + x) + x(0.5 + x)) = 15.75
((0.5 * 0.5 + x * 0.5) + x(0.5 + x)) = 15.75
((0.25 + 0.5x) + x(0.5 + x)) = 15.75
(0.25 + 0.5x + (0.5 * x + x * x)) = 15.75
(0.25 + 0.5x + (0.5x + x2)) = 15.75

Combine like terms: 0.5x + 0.5x = 1x
(0.25 + 1x + x2) = 15.75

Solving
0.25 + 1x + x2 = 15.75

Solving for variable 'x'.

Reorder the terms:
0.25 + -15.75 + 1x + x2 = 15.75 + -15.75

Combine like terms: 0.25 + -15.75 = -15.5
-15.5 + 1x + x2 = 15.75 + -15.75

Combine like terms: 15.75 + -15.75 = 0.00
-15.5 + 1x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '15.5' to each side of the equation.
-15.5 + 1x + 15.5 + x2 = 0.00 + 15.5

Reorder the terms:
-15.5 + 15.5 + 1x + x2 = 0.00 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + 1x + x2 = 0.00 + 15.5
1x + x2 = 0.00 + 15.5

Combine like terms: 0.00 + 15.5 = 15.5
1x + x2 = 15.5

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.
x + 0.25 + x2 = 15.5 + 0.25

Reorder the terms:
0.25 + x + x2 = 15.5 + 0.25

Combine like terms: 15.5 + 0.25 = 15.75
0.25 + x + x2 = 15.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.968626967 and -3.968626967.


Subproblem 1
x + 0.5 = 3.968626967

Simplifying
x + 0.5 = 3.968626967

Reorder the terms:
0.5 + x = 3.968626967

Solving
0.5 + x = 3.968626967

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 = 3.968626967 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.968626967 + -0.5
x = 3.968626967 + -0.5

Combine like terms: 3.968626967 + -0.5 = 3.468626967
x = 3.468626967

Simplifying
x = 3.468626967


Subproblem 2
x + 0.5 = -3.968626967

Simplifying
x + 0.5 = -3.968626967

Reorder the terms:
0.5 + x = -3.968626967

Solving
0.5 + x = -3.968626967

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 = -3.968626967 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.968626967 + -0.5
x = -3.968626967 + -0.5

Combine like terms: -3.968626967 + -0.5 = -4.468626967
x = -4.468626967

Simplifying
x = -4.468626967


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.468626967, -4.468626967}

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