3x^2-42x+126=0

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Solution for 3x^2-42x+126=0 equation: 


Simplifying
3x2 + -42x + 126 = 0

Reorder the terms:
126 + -42x + 3x2 = 0

Solving
126 + -42x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(42 + -14x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(42 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
42 + -14x + x2 = 0

Solving
42 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -14x + -42 + x2 = 0 + -42

Reorder the terms:
42 + -42 + -14x + x2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -14x + x2 = 0 + -42
-14x + x2 = 0 + -42

Combine like terms: 0 + -42 = -42
-14x + x2 = -42

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 = -42 + 49

Reorder the terms:
49 + -14x + x2 = -42 + 49

Combine like terms: -42 + 49 = 7
49 + -14x + x2 = 7

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

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -7) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + -7 = 2.645751311

Simplifying
x + -7 = 2.645751311

Reorder the terms:
-7 + x = 2.645751311

Solving
-7 + x = 2.645751311

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 = 2.645751311 + 7

Combine like terms: -7 + 7 = 0
0 + x = 2.645751311 + 7
x = 2.645751311 + 7

Combine like terms: 2.645751311 + 7 = 9.645751311
x = 9.645751311

Simplifying
x = 9.645751311


Subproblem 2
x + -7 = -2.645751311

Simplifying
x + -7 = -2.645751311

Reorder the terms:
-7 + x = -2.645751311

Solving
-7 + x = -2.645751311

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 = -2.645751311 + 7

Combine like terms: -7 + 7 = 0
0 + x = -2.645751311 + 7
x = -2.645751311 + 7

Combine like terms: -2.645751311 + 7 = 4.354248689
x = 4.354248689

Simplifying
x = 4.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.645751311, 4.354248689}
Solution
x = {9.645751311, 4.354248689}

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