5x^2-55x+100=0

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Solution for 5x^2-55x+100=0 equation: 


Simplifying
5x2 + -55x + 100 = 0

Reorder the terms:
100 + -55x + 5x2 = 0

Solving
100 + -55x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(20 + -11x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(20 + -11x + x2)' equal to zero and attempt to solve:

Simplifying
20 + -11x + x2 = 0

Solving
20 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -11x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -11x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -11x + x2 = 0 + -20
-11x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-11x + x2 = -20

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 = -20 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -20 + 30.25

Combine like terms: -20 + 30.25 = 10.25
30.25 + -11x + x2 = 10.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -5.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + -5.5 = 3.201562119

Simplifying
x + -5.5 = 3.201562119

Reorder the terms:
-5.5 + x = 3.201562119

Solving
-5.5 + x = 3.201562119

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 = 3.201562119 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 3.201562119 + 5.5
x = 3.201562119 + 5.5

Combine like terms: 3.201562119 + 5.5 = 8.701562119
x = 8.701562119

Simplifying
x = 8.701562119


Subproblem 2
x + -5.5 = -3.201562119

Simplifying
x + -5.5 = -3.201562119

Reorder the terms:
-5.5 + x = -3.201562119

Solving
-5.5 + x = -3.201562119

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 = -3.201562119 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -3.201562119 + 5.5
x = -3.201562119 + 5.5

Combine like terms: -3.201562119 + 5.5 = 2.298437881
x = 2.298437881

Simplifying
x = 2.298437881


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.701562119, 2.298437881}
Solution
x = {8.701562119, 2.298437881}

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