6x^2-84x+160=0

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Solution for 6x^2-84x+160=0 equation: 


Simplifying
6x2 + -84x + 160 = 0

Reorder the terms:
160 + -84x + 6x2 = 0

Solving
160 + -84x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(80 + -42x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(80 + -42x + 3x2)' equal to zero and attempt to solve:

Simplifying
80 + -42x + 3x2 = 0

Solving
80 + -42x + 3x2 = 0

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

Divide each side by '3'.
26.66666667 + -14x + x2 = 0

Move the constant term to the right:

Add '-26.66666667' to each side of the equation.
26.66666667 + -14x + -26.66666667 + x2 = 0 + -26.66666667

Reorder the terms:
26.66666667 + -26.66666667 + -14x + x2 = 0 + -26.66666667

Combine like terms: 26.66666667 + -26.66666667 = 0.00000000
0.00000000 + -14x + x2 = 0 + -26.66666667
-14x + x2 = 0 + -26.66666667

Combine like terms: 0 + -26.66666667 = -26.66666667
-14x + x2 = -26.66666667

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -26.66666667 + 49

Reorder the terms:
49 + -14x + x2 = -26.66666667 + 49

Combine like terms: -26.66666667 + 49 = 22.33333333
49 + -14x + x2 = 22.33333333

Factor a perfect square on the left side:
(x + -7)(x + -7) = 22.33333333

Calculate the square root of the right side: 4.725815626

Break this problem into two subproblems by setting 
(x + -7) equal to 4.725815626 and -4.725815626.


Subproblem 1
x + -7 = 4.725815626

Simplifying
x + -7 = 4.725815626

Reorder the terms:
-7 + x = 4.725815626

Solving
-7 + x = 4.725815626

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 4.725815626 + 7

Combine like terms: -7 + 7 = 0
0 + x = 4.725815626 + 7
x = 4.725815626 + 7

Combine like terms: 4.725815626 + 7 = 11.725815626
x = 11.725815626

Simplifying
x = 11.725815626


Subproblem 2
x + -7 = -4.725815626

Simplifying
x + -7 = -4.725815626

Reorder the terms:
-7 + x = -4.725815626

Solving
-7 + x = -4.725815626

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -4.725815626 + 7

Combine like terms: -7 + 7 = 0
0 + x = -4.725815626 + 7
x = -4.725815626 + 7

Combine like terms: -4.725815626 + 7 = 2.274184374
x = 2.274184374

Simplifying
x = 2.274184374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.725815626, 2.274184374}
Solution
x = {11.725815626, 2.274184374}

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