6x^2-60x+94=300

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Solution for 6x^2-60x+94=300 equation: 


Simplifying
6x2 + -60x + 94 = 300

Reorder the terms:
94 + -60x + 6x2 = 300

Solving
94 + -60x + 6x2 = 300

Solving for variable 'x'.

Reorder the terms:
94 + -300 + -60x + 6x2 = 300 + -300

Combine like terms: 94 + -300 = -206
-206 + -60x + 6x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-206 + -60x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-103 + -30x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-103 + -30x + 3x2)' equal to zero and attempt to solve:

Simplifying
-103 + -30x + 3x2 = 0

Solving
-103 + -30x + 3x2 = 0

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

Divide each side by '3'.
-34.33333333 + -10x + x2 = 0

Move the constant term to the right:

Add '34.33333333' to each side of the equation.
-34.33333333 + -10x + 34.33333333 + x2 = 0 + 34.33333333

Reorder the terms:
-34.33333333 + 34.33333333 + -10x + x2 = 0 + 34.33333333

Combine like terms: -34.33333333 + 34.33333333 = 0.00000000
0.00000000 + -10x + x2 = 0 + 34.33333333
-10x + x2 = 0 + 34.33333333

Combine like terms: 0 + 34.33333333 = 34.33333333
-10x + x2 = 34.33333333

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 34.33333333 + 25

Reorder the terms:
25 + -10x + x2 = 34.33333333 + 25

Combine like terms: 34.33333333 + 25 = 59.33333333
25 + -10x + x2 = 59.33333333

Factor a perfect square on the left side:
(x + -5)(x + -5) = 59.33333333

Calculate the square root of the right side: 7.702813339

Break this problem into two subproblems by setting 
(x + -5) equal to 7.702813339 and -7.702813339.


Subproblem 1
x + -5 = 7.702813339

Simplifying
x + -5 = 7.702813339

Reorder the terms:
-5 + x = 7.702813339

Solving
-5 + x = 7.702813339

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 7.702813339 + 5

Combine like terms: -5 + 5 = 0
0 + x = 7.702813339 + 5
x = 7.702813339 + 5

Combine like terms: 7.702813339 + 5 = 12.702813339
x = 12.702813339

Simplifying
x = 12.702813339


Subproblem 2
x + -5 = -7.702813339

Simplifying
x + -5 = -7.702813339

Reorder the terms:
-5 + x = -7.702813339

Solving
-5 + x = -7.702813339

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -7.702813339 + 5

Combine like terms: -5 + 5 = 0
0 + x = -7.702813339 + 5
x = -7.702813339 + 5

Combine like terms: -7.702813339 + 5 = -2.702813339
x = -2.702813339

Simplifying
x = -2.702813339


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.702813339, -2.702813339}
Solution
x = {12.702813339, -2.702813339}

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