3x^2-84x+546=0

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Solution for 3x^2-84x+546=0 equation: 


Simplifying
3x2 + -84x + 546 = 0

Reorder the terms:
546 + -84x + 3x2 = 0

Solving
546 + -84x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(182 + -28x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(182 + -28x + x2)' equal to zero and attempt to solve:

Simplifying
182 + -28x + x2 = 0

Solving
182 + -28x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-182' to each side of the equation.
182 + -28x + -182 + x2 = 0 + -182

Reorder the terms:
182 + -182 + -28x + x2 = 0 + -182

Combine like terms: 182 + -182 = 0
0 + -28x + x2 = 0 + -182
-28x + x2 = 0 + -182

Combine like terms: 0 + -182 = -182
-28x + x2 = -182

The x term is -28x.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28x + 196 + x2 = -182 + 196

Reorder the terms:
196 + -28x + x2 = -182 + 196

Combine like terms: -182 + 196 = 14
196 + -28x + x2 = 14

Factor a perfect square on the left side:
(x + -14)(x + -14) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -14) equal to 3.741657387 and -3.741657387.


Subproblem 1
x + -14 = 3.741657387

Simplifying
x + -14 = 3.741657387

Reorder the terms:
-14 + x = 3.741657387

Solving
-14 + x = 3.741657387

Solving for variable 'x'.

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

Add '14' to each side of the equation.
-14 + 14 + x = 3.741657387 + 14

Combine like terms: -14 + 14 = 0
0 + x = 3.741657387 + 14
x = 3.741657387 + 14

Combine like terms: 3.741657387 + 14 = 17.741657387
x = 17.741657387

Simplifying
x = 17.741657387


Subproblem 2
x + -14 = -3.741657387

Simplifying
x + -14 = -3.741657387

Reorder the terms:
-14 + x = -3.741657387

Solving
-14 + x = -3.741657387

Solving for variable 'x'.

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

Add '14' to each side of the equation.
-14 + 14 + x = -3.741657387 + 14

Combine like terms: -14 + 14 = 0
0 + x = -3.741657387 + 14
x = -3.741657387 + 14

Combine like terms: -3.741657387 + 14 = 10.258342613
x = 10.258342613

Simplifying
x = 10.258342613


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.741657387, 10.258342613}
Solution
x = {17.741657387, 10.258342613}

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