2.5x^2+220x-120=0

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Solution for 2.5x^2+220x-120=0 equation: 


Simplifying
2.5x2 + 220x + -120 = 0

Reorder the terms:
-120 + 220x + 2.5x2 = 0

Solving
-120 + 220x + 2.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.5'.
-48 + 88x + x2 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 88x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 88x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 88x + x2 = 0 + 48
88x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
88x + x2 = 48

The x term is 88x.  Take half its coefficient (44).
Square it (1936) and add it to both sides.

Add '1936' to each side of the equation.
88x + 1936 + x2 = 48 + 1936

Reorder the terms:
1936 + 88x + x2 = 48 + 1936

Combine like terms: 48 + 1936 = 1984
1936 + 88x + x2 = 1984

Factor a perfect square on the left side:
(x + 44)(x + 44) = 1984

Calculate the square root of the right side: 44.542114903

Break this problem into two subproblems by setting 
(x + 44) equal to 44.542114903 and -44.542114903.


Subproblem 1
x + 44 = 44.542114903

Simplifying
x + 44 = 44.542114903

Reorder the terms:
44 + x = 44.542114903

Solving
44 + x = 44.542114903

Solving for variable 'x'.

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

Add '-44' to each side of the equation.
44 + -44 + x = 44.542114903 + -44

Combine like terms: 44 + -44 = 0
0 + x = 44.542114903 + -44
x = 44.542114903 + -44

Combine like terms: 44.542114903 + -44 = 0.542114903
x = 0.542114903

Simplifying
x = 0.542114903


Subproblem 2
x + 44 = -44.542114903

Simplifying
x + 44 = -44.542114903

Reorder the terms:
44 + x = -44.542114903

Solving
44 + x = -44.542114903

Solving for variable 'x'.

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

Add '-44' to each side of the equation.
44 + -44 + x = -44.542114903 + -44

Combine like terms: 44 + -44 = 0
0 + x = -44.542114903 + -44
x = -44.542114903 + -44

Combine like terms: -44.542114903 + -44 = -88.542114903
x = -88.542114903

Simplifying
x = -88.542114903


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.542114903, -88.542114903}

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