x^2+5.5x-15=0

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Solution for x^2+5.5x-15=0 equation: 


Simplifying
x2 + 5.5x + -15 = 0

Reorder the terms:
-15 + 5.5x + x2 = 0

Solving
-15 + 5.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 5.5x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 5.5x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 5.5x + x2 = 0 + 15
5.5x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
5.5x + x2 = 15

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 = 15 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 15 + 7.5625

Combine like terms: 15 + 7.5625 = 22.5625
7.5625 + 5.5x + x2 = 22.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 22.5625

Calculate the square root of the right side: 4.75

Break this problem into two subproblems by setting 
(x + 2.75) equal to 4.75 and -4.75.


Subproblem 1
x + 2.75 = 4.75

Simplifying
x + 2.75 = 4.75

Reorder the terms:
2.75 + x = 4.75

Solving
2.75 + x = 4.75

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 = 4.75 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 4.75 + -2.75
x = 4.75 + -2.75

Combine like terms: 4.75 + -2.75 = 2
x = 2

Simplifying
x = 2


Subproblem 2
x + 2.75 = -4.75

Simplifying
x + 2.75 = -4.75

Reorder the terms:
2.75 + x = -4.75

Solving
2.75 + x = -4.75

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 = -4.75 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -4.75 + -2.75
x = -4.75 + -2.75

Combine like terms: -4.75 + -2.75 = -7.5
x = -7.5

Simplifying
x = -7.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, -7.5}

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