3x^2-42x+42=0

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


Simplifying
3x2 + -42x + 42 = 0

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

Solving
42 + -42x + 3x2 = 0

Solving for variable 'x'.

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

Ignore the factor 3.

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

Simplifying
14 + -14x + x2 = 0

Solving
14 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -14 + 49

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

Combine like terms: -14 + 49 = 35
49 + -14x + x2 = 35

Factor a perfect square on the left side:
(x + -7)(x + -7) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(x + -7) equal to 5.916079783 and -5.916079783.


Subproblem 1
x + -7 = 5.916079783

Simplifying
x + -7 = 5.916079783

Reorder the terms:
-7 + x = 5.916079783

Solving
-7 + x = 5.916079783

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 = 5.916079783 + 7

Combine like terms: -7 + 7 = 0
0 + x = 5.916079783 + 7
x = 5.916079783 + 7

Combine like terms: 5.916079783 + 7 = 12.916079783
x = 12.916079783

Simplifying
x = 12.916079783


Subproblem 2
x + -7 = -5.916079783

Simplifying
x + -7 = -5.916079783

Reorder the terms:
-7 + x = -5.916079783

Solving
-7 + x = -5.916079783

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 = -5.916079783 + 7

Combine like terms: -7 + 7 = 0
0 + x = -5.916079783 + 7
x = -5.916079783 + 7

Combine like terms: -5.916079783 + 7 = 1.083920217
x = 1.083920217

Simplifying
x = 1.083920217


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.916079783, 1.083920217}
Solution
x = {12.916079783, 1.083920217}

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