-6x^2+41x+63=0

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Solution for -6x^2+41x+63=0 equation: 


Simplifying
-6x2 + 41x + 63 = 0

Reorder the terms:
63 + 41x + -6x2 = 0

Solving
63 + 41x + -6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-10.5 + -6.833333333x + x2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + -6.833333333x + 10.5 + x2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + -6.833333333x + x2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + -6.833333333x + x2 = 0 + 10.5
-6.833333333x + x2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
-6.833333333x + x2 = 10.5

The x term is -6.833333333x.  Take half its coefficient (-3.416666667).
Square it (11.67361111) and add it to both sides.

Add '11.67361111' to each side of the equation.
-6.833333333x + 11.67361111 + x2 = 10.5 + 11.67361111

Reorder the terms:
11.67361111 + -6.833333333x + x2 = 10.5 + 11.67361111

Combine like terms: 10.5 + 11.67361111 = 22.17361111
11.67361111 + -6.833333333x + x2 = 22.17361111

Factor a perfect square on the left side:
(x + -3.416666667)(x + -3.416666667) = 22.17361111

Calculate the square root of the right side: 4.708886398

Break this problem into two subproblems by setting 
(x + -3.416666667) equal to 4.708886398 and -4.708886398.


Subproblem 1
x + -3.416666667 = 4.708886398

Simplifying
x + -3.416666667 = 4.708886398

Reorder the terms:
-3.416666667 + x = 4.708886398

Solving
-3.416666667 + x = 4.708886398

Solving for variable 'x'.

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

Add '3.416666667' to each side of the equation.
-3.416666667 + 3.416666667 + x = 4.708886398 + 3.416666667

Combine like terms: -3.416666667 + 3.416666667 = 0.000000000
0.000000000 + x = 4.708886398 + 3.416666667
x = 4.708886398 + 3.416666667

Combine like terms: 4.708886398 + 3.416666667 = 8.125553065
x = 8.125553065

Simplifying
x = 8.125553065


Subproblem 2
x + -3.416666667 = -4.708886398

Simplifying
x + -3.416666667 = -4.708886398

Reorder the terms:
-3.416666667 + x = -4.708886398

Solving
-3.416666667 + x = -4.708886398

Solving for variable 'x'.

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

Add '3.416666667' to each side of the equation.
-3.416666667 + 3.416666667 + x = -4.708886398 + 3.416666667

Combine like terms: -3.416666667 + 3.416666667 = 0.000000000
0.000000000 + x = -4.708886398 + 3.416666667
x = -4.708886398 + 3.416666667

Combine like terms: -4.708886398 + 3.416666667 = -1.292219731
x = -1.292219731

Simplifying
x = -1.292219731


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.125553065, -1.292219731}

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