3x^2-42x-174=0

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Solution for 3x^2-42x-174=0 equation: 


Simplifying
3x2 + -42x + -174 = 0

Reorder the terms:
-174 + -42x + 3x2 = 0

Solving
-174 + -42x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-58 + -14x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-58 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
-58 + -14x + x2 = 0

Solving
-58 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '58' to each side of the equation.
-58 + -14x + 58 + x2 = 0 + 58

Reorder the terms:
-58 + 58 + -14x + x2 = 0 + 58

Combine like terms: -58 + 58 = 0
0 + -14x + x2 = 0 + 58
-14x + x2 = 0 + 58

Combine like terms: 0 + 58 = 58
-14x + x2 = 58

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 = 58 + 49

Reorder the terms:
49 + -14x + x2 = 58 + 49

Combine like terms: 58 + 49 = 107
49 + -14x + x2 = 107

Factor a perfect square on the left side:
(x + -7)(x + -7) = 107

Calculate the square root of the right side: 10.344080433

Break this problem into two subproblems by setting 
(x + -7) equal to 10.344080433 and -10.344080433.


Subproblem 1
x + -7 = 10.344080433

Simplifying
x + -7 = 10.344080433

Reorder the terms:
-7 + x = 10.344080433

Solving
-7 + x = 10.344080433

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 = 10.344080433 + 7

Combine like terms: -7 + 7 = 0
0 + x = 10.344080433 + 7
x = 10.344080433 + 7

Combine like terms: 10.344080433 + 7 = 17.344080433
x = 17.344080433

Simplifying
x = 17.344080433


Subproblem 2
x + -7 = -10.344080433

Simplifying
x + -7 = -10.344080433

Reorder the terms:
-7 + x = -10.344080433

Solving
-7 + x = -10.344080433

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 = -10.344080433 + 7

Combine like terms: -7 + 7 = 0
0 + x = -10.344080433 + 7
x = -10.344080433 + 7

Combine like terms: -10.344080433 + 7 = -3.344080433
x = -3.344080433

Simplifying
x = -3.344080433


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.344080433, -3.344080433}
Solution
x = {17.344080433, -3.344080433}

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