x^2+15x+55=0

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Solution for x^2+15x+55=0 equation: 


Simplifying
x2 + 15x + 55 = 0

Reorder the terms:
55 + 15x + x2 = 0

Solving
55 + 15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-55' to each side of the equation.
55 + 15x + -55 + x2 = 0 + -55

Reorder the terms:
55 + -55 + 15x + x2 = 0 + -55

Combine like terms: 55 + -55 = 0
0 + 15x + x2 = 0 + -55
15x + x2 = 0 + -55

Combine like terms: 0 + -55 = -55
15x + x2 = -55

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -55 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -55 + 56.25

Combine like terms: -55 + 56.25 = 1.25
56.25 + 15x + x2 = 1.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 7.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
x + 7.5 = 1.118033989

Simplifying
x + 7.5 = 1.118033989

Reorder the terms:
7.5 + x = 1.118033989

Solving
7.5 + x = 1.118033989

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 1.118033989 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 1.118033989 + -7.5
x = 1.118033989 + -7.5

Combine like terms: 1.118033989 + -7.5 = -6.381966011
x = -6.381966011

Simplifying
x = -6.381966011


Subproblem 2
x + 7.5 = -1.118033989

Simplifying
x + 7.5 = -1.118033989

Reorder the terms:
7.5 + x = -1.118033989

Solving
7.5 + x = -1.118033989

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -1.118033989 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -1.118033989 + -7.5
x = -1.118033989 + -7.5

Combine like terms: -1.118033989 + -7.5 = -8.618033989
x = -8.618033989

Simplifying
x = -8.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-6.381966011, -8.618033989}

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