5X^2+55X-120=0

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Solution for 5X^2+55X-120=0 equation:


Simplifying
5X2 + 55X + -120 = 0

Reorder the terms:
-120 + 55X + 5X2 = 0

Solving
-120 + 55X + 5X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-24 + 11X + X2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-24 + 11X + X2)' equal to zero and attempt to solve:

Simplifying
-24 + 11X + X2 = 0

Solving
-24 + 11X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 11X + 24 + X2 = 0 + 24

Reorder the terms:
-24 + 24 + 11X + X2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 11X + X2 = 0 + 24
11X + X2 = 0 + 24

Combine like terms: 0 + 24 = 24
11X + X2 = 24

The X term is 11X.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11X + 30.25 + X2 = 24 + 30.25

Reorder the terms:
30.25 + 11X + X2 = 24 + 30.25

Combine like terms: 24 + 30.25 = 54.25
30.25 + 11X + X2 = 54.25

Factor a perfect square on the left side:
(X + 5.5)(X + 5.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(X + 5.5) equal to 7.365459931 and -7.365459931.


Subproblem 1
X + 5.5 = 7.365459931

Simplifying
X + 5.5 = 7.365459931

Reorder the terms:
5.5 + X = 7.365459931

Solving
5.5 + X = 7.365459931

Solving for variable 'X'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + X = 7.365459931 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + X = 7.365459931 + -5.5
X = 7.365459931 + -5.5

Combine like terms: 7.365459931 + -5.5 = 1.865459931
X = 1.865459931

Simplifying
X = 1.865459931


Subproblem 2
X + 5.5 = -7.365459931

Simplifying
X + 5.5 = -7.365459931

Reorder the terms:
5.5 + X = -7.365459931

Solving
5.5 + X = -7.365459931

Solving for variable 'X'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + X = -7.365459931 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + X = -7.365459931 + -5.5
X = -7.365459931 + -5.5

Combine like terms: -7.365459931 + -5.5 = -12.865459931
X = -12.865459931

Simplifying
X = -12.865459931


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.865459931, -12.865459931}
Solution
X = {1.865459931, -12.865459931}

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