16=(x+0.5)(x+0.5)

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Solution for 16=(x+0.5)(x+0.5) equation: 


Simplifying
16 = (x + 0.5)(x + 0.5)

Reorder the terms:
16 = (0.5 + x)(x + 0.5)

Reorder the terms:
16 = (0.5 + x)(0.5 + x)

Multiply (0.5 + x) * (0.5 + x)
16 = (0.5(0.5 + x) + x(0.5 + x))
16 = ((0.5 * 0.5 + x * 0.5) + x(0.5 + x))
16 = ((0.25 + 0.5x) + x(0.5 + x))
16 = (0.25 + 0.5x + (0.5 * x + x * x))
16 = (0.25 + 0.5x + (0.5x + x2))

Combine like terms: 0.5x + 0.5x = 1x
16 = (0.25 + 1x + x2)

Solving
16 = 0.25 + 1x + x2

Solving for variable 'x'.

Combine like terms: 16 + -0.25 = 15.75
15.75 + -1x + -1x2 = 0.25 + 1x + x2 + -0.25 + -1x + -1x2

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

Combine like terms: 0.25 + -0.25 = 0.00
15.75 + -1x + -1x2 = 0.00 + 1x + -1x + x2 + -1x2
15.75 + -1x + -1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
15.75 + -1x + -1x2 = 0 + x2 + -1x2
15.75 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15.75 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-15.75 + x + x2 = 0

Move the constant term to the right:

Add '15.75' to each side of the equation.
-15.75 + x + 15.75 + x2 = 0 + 15.75

Reorder the terms:
-15.75 + 15.75 + x + x2 = 0 + 15.75

Combine like terms: -15.75 + 15.75 = 0.00
0.00 + x + x2 = 0 + 15.75
x + x2 = 0 + 15.75

Combine like terms: 0 + 15.75 = 15.75
x + x2 = 15.75

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.
 + 0.25 + x2 = 15.75 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 15.75 + 0.25

Combine like terms: 15.75 + 0.25 = 16
1.25 + x2 = 16

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4 and -4.


Subproblem 1
x + 0.5 = 4

Simplifying
x + 0.5 = 4

Reorder the terms:
0.5 + x = 4

Solving
0.5 + x = 4

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 = 4 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4 + -0.5
x = 4 + -0.5

Combine like terms: 4 + -0.5 = 3.5
x = 3.5

Simplifying
x = 3.5


Subproblem 2
x + 0.5 = -4

Simplifying
x + 0.5 = -4

Reorder the terms:
0.5 + x = -4

Solving
0.5 + x = -4

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 = -4 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4 + -0.5
x = -4 + -0.5

Combine like terms: -4 + -0.5 = -4.5
x = -4.5

Simplifying
x = -4.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5, -4.5}

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