3x^2-120x+300=0

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Solution for 3x^2-120x+300=0 equation: 


Simplifying
3x2 + -120x + 300 = 0

Reorder the terms:
300 + -120x + 3x2 = 0

Solving
300 + -120x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(100 + -40x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(100 + -40x + x2)' equal to zero and attempt to solve:

Simplifying
100 + -40x + x2 = 0

Solving
100 + -40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -40x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + -40x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -40x + x2 = 0 + -100
-40x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
-40x + x2 = -100

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = -100 + 400

Reorder the terms:
400 + -40x + x2 = -100 + 400

Combine like terms: -100 + 400 = 300
400 + -40x + x2 = 300

Factor a perfect square on the left side:
(x + -20)(x + -20) = 300

Calculate the square root of the right side: 17.320508076

Break this problem into two subproblems by setting 
(x + -20) equal to 17.320508076 and -17.320508076.


Subproblem 1
x + -20 = 17.320508076

Simplifying
x + -20 = 17.320508076

Reorder the terms:
-20 + x = 17.320508076

Solving
-20 + x = 17.320508076

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = 17.320508076 + 20

Combine like terms: -20 + 20 = 0
0 + x = 17.320508076 + 20
x = 17.320508076 + 20

Combine like terms: 17.320508076 + 20 = 37.320508076
x = 37.320508076

Simplifying
x = 37.320508076


Subproblem 2
x + -20 = -17.320508076

Simplifying
x + -20 = -17.320508076

Reorder the terms:
-20 + x = -17.320508076

Solving
-20 + x = -17.320508076

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = -17.320508076 + 20

Combine like terms: -20 + 20 = 0
0 + x = -17.320508076 + 20
x = -17.320508076 + 20

Combine like terms: -17.320508076 + 20 = 2.679491924
x = 2.679491924

Simplifying
x = 2.679491924


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {37.320508076, 2.679491924}
Solution
x = {37.320508076, 2.679491924}

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