6x^2-120x=600

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Solution for 6x^2-120x=600 equation: 


Simplifying
6x2 + -120x = 600

Reorder the terms:
-120x + 6x2 = 600

Solving
-120x + 6x2 = 600

Solving for variable 'x'.

Reorder the terms:
-600 + -120x + 6x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-600 + -120x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-100 + -20x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-100 + -20x + x2)' equal to zero and attempt to solve:

Simplifying
-100 + -20x + x2 = 0

Solving
-100 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -20x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + -20x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -20x + x2 = 0 + 100
-20x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
-20x + x2 = 100

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 100 + 100

Reorder the terms:
100 + -20x + x2 = 100 + 100

Combine like terms: 100 + 100 = 200
100 + -20x + x2 = 200

Factor a perfect square on the left side:
(x + -10)(x + -10) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(x + -10) equal to 14.142135624 and -14.142135624.


Subproblem 1
x + -10 = 14.142135624

Simplifying
x + -10 = 14.142135624

Reorder the terms:
-10 + x = 14.142135624

Solving
-10 + x = 14.142135624

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 14.142135624 + 10

Combine like terms: -10 + 10 = 0
0 + x = 14.142135624 + 10
x = 14.142135624 + 10

Combine like terms: 14.142135624 + 10 = 24.142135624
x = 24.142135624

Simplifying
x = 24.142135624


Subproblem 2
x + -10 = -14.142135624

Simplifying
x + -10 = -14.142135624

Reorder the terms:
-10 + x = -14.142135624

Solving
-10 + x = -14.142135624

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -14.142135624 + 10

Combine like terms: -10 + 10 = 0
0 + x = -14.142135624 + 10
x = -14.142135624 + 10

Combine like terms: -14.142135624 + 10 = -4.142135624
x = -4.142135624

Simplifying
x = -4.142135624


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.142135624, -4.142135624}
Solution
x = {24.142135624, -4.142135624}

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