8.3=x(x+5.5)

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Solution for 8.3=x(x+5.5) equation: 


Simplifying
8.3 = x(x + 5.5)

Reorder the terms:
8.3 = x(5.5 + x)
8.3 = (5.5 * x + x * x)
8.3 = (5.5x + x2)

Solving
8.3 = 5.5x + x2

Solving for variable 'x'.

Reorder the terms:
8.3 + -5.5x + -1x2 = 5.5x + -5.5x + x2 + -1x2

Combine like terms: 5.5x + -5.5x = 0.0
8.3 + -5.5x + -1x2 = 0.0 + x2 + -1x2
8.3 + -5.5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8.3 + -5.5x + -1x2 = 0

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

Divide each side by '-1'.
-8.3 + 5.5x + x2 = 0

Move the constant term to the right:

Add '8.3' to each side of the equation.
-8.3 + 5.5x + 8.3 + x2 = 0 + 8.3

Reorder the terms:
-8.3 + 8.3 + 5.5x + x2 = 0 + 8.3

Combine like terms: -8.3 + 8.3 = 0.0
0.0 + 5.5x + x2 = 0 + 8.3
5.5x + x2 = 0 + 8.3

Combine like terms: 0 + 8.3 = 8.3
5.5x + x2 = 8.3

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 8.3 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 8.3 + 7.5625

Combine like terms: 8.3 + 7.5625 = 15.8625
7.5625 + 5.5x + x2 = 15.8625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 15.8625

Calculate the square root of the right side: 3.982775414

Break this problem into two subproblems by setting 
(x + 2.75) equal to 3.982775414 and -3.982775414.


Subproblem 1
x + 2.75 = 3.982775414

Simplifying
x + 2.75 = 3.982775414

Reorder the terms:
2.75 + x = 3.982775414

Solving
2.75 + x = 3.982775414

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 3.982775414 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 3.982775414 + -2.75
x = 3.982775414 + -2.75

Combine like terms: 3.982775414 + -2.75 = 1.232775414
x = 1.232775414

Simplifying
x = 1.232775414


Subproblem 2
x + 2.75 = -3.982775414

Simplifying
x + 2.75 = -3.982775414

Reorder the terms:
2.75 + x = -3.982775414

Solving
2.75 + x = -3.982775414

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -3.982775414 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -3.982775414 + -2.75
x = -3.982775414 + -2.75

Combine like terms: -3.982775414 + -2.75 = -6.732775414
x = -6.732775414

Simplifying
x = -6.732775414


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.232775414, -6.732775414}

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