3x^2-42x-117=0

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Solution for 3x^2-42x-117=0 equation: 


Simplifying
3x2 + -42x + -117 = 0

Reorder the terms:
-117 + -42x + 3x2 = 0

Solving
-117 + -42x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-39 + -14x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-39 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
-39 + -14x + x2 = 0

Solving
-39 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + -14x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + -14x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -14x + x2 = 0 + 39
-14x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
-14x + x2 = 39

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 = 39 + 49

Reorder the terms:
49 + -14x + x2 = 39 + 49

Combine like terms: 39 + 49 = 88
49 + -14x + x2 = 88

Factor a perfect square on the left side:
(x + -7)(x + -7) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(x + -7) equal to 9.38083152 and -9.38083152.


Subproblem 1
x + -7 = 9.38083152

Simplifying
x + -7 = 9.38083152

Reorder the terms:
-7 + x = 9.38083152

Solving
-7 + x = 9.38083152

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 = 9.38083152 + 7

Combine like terms: -7 + 7 = 0
0 + x = 9.38083152 + 7
x = 9.38083152 + 7

Combine like terms: 9.38083152 + 7 = 16.38083152
x = 16.38083152

Simplifying
x = 16.38083152


Subproblem 2
x + -7 = -9.38083152

Simplifying
x + -7 = -9.38083152

Reorder the terms:
-7 + x = -9.38083152

Solving
-7 + x = -9.38083152

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 = -9.38083152 + 7

Combine like terms: -7 + 7 = 0
0 + x = -9.38083152 + 7
x = -9.38083152 + 7

Combine like terms: -9.38083152 + 7 = -2.38083152
x = -2.38083152

Simplifying
x = -2.38083152


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.38083152, -2.38083152}
Solution
x = {16.38083152, -2.38083152}

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