x^2+15x+7.5=0

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Solution for x^2+15x+7.5=0 equation: 


Simplifying
x2 + 15x + 7.5 = 0

Reorder the terms:
7.5 + 15x + x2 = 0

Solving
7.5 + 15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-7.5' to each side of the equation.
7.5 + 15x + -7.5 + x2 = 0 + -7.5

Reorder the terms:
7.5 + -7.5 + 15x + x2 = 0 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + 15x + x2 = 0 + -7.5
15x + x2 = 0 + -7.5

Combine like terms: 0 + -7.5 = -7.5
15x + x2 = -7.5

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 = -7.5 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -7.5 + 56.25

Combine like terms: -7.5 + 56.25 = 48.75
56.25 + 15x + x2 = 48.75

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 48.75

Calculate the square root of the right side: 6.982120022

Break this problem into two subproblems by setting 
(x + 7.5) equal to 6.982120022 and -6.982120022.


Subproblem 1
x + 7.5 = 6.982120022

Simplifying
x + 7.5 = 6.982120022

Reorder the terms:
7.5 + x = 6.982120022

Solving
7.5 + x = 6.982120022

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 = 6.982120022 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 6.982120022 + -7.5
x = 6.982120022 + -7.5

Combine like terms: 6.982120022 + -7.5 = -0.517879978
x = -0.517879978

Simplifying
x = -0.517879978


Subproblem 2
x + 7.5 = -6.982120022

Simplifying
x + 7.5 = -6.982120022

Reorder the terms:
7.5 + x = -6.982120022

Solving
7.5 + x = -6.982120022

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 = -6.982120022 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -6.982120022 + -7.5
x = -6.982120022 + -7.5

Combine like terms: -6.982120022 + -7.5 = -14.482120022
x = -14.482120022

Simplifying
x = -14.482120022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.517879978, -14.482120022}

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