3x^2-42x+105=0

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Solution for 3x^2-42x+105=0 equation: 


Simplifying
3x2 + -42x + 105 = 0

Reorder the terms:
105 + -42x + 3x2 = 0

Solving
105 + -42x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(35 + -14x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(35 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
35 + -14x + x2 = 0

Solving
35 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -14x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + -14x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -14x + x2 = 0 + -35
-14x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
-14x + x2 = -35

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 = -35 + 49

Reorder the terms:
49 + -14x + x2 = -35 + 49

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

Factor a perfect square on the left side:
(x + -7)(x + -7) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -7) equal to 3.741657387 and -3.741657387.


Subproblem 1
x + -7 = 3.741657387

Simplifying
x + -7 = 3.741657387

Reorder the terms:
-7 + x = 3.741657387

Solving
-7 + x = 3.741657387

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 = 3.741657387 + 7

Combine like terms: -7 + 7 = 0
0 + x = 3.741657387 + 7
x = 3.741657387 + 7

Combine like terms: 3.741657387 + 7 = 10.741657387
x = 10.741657387

Simplifying
x = 10.741657387


Subproblem 2
x + -7 = -3.741657387

Simplifying
x + -7 = -3.741657387

Reorder the terms:
-7 + x = -3.741657387

Solving
-7 + x = -3.741657387

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 = -3.741657387 + 7

Combine like terms: -7 + 7 = 0
0 + x = -3.741657387 + 7
x = -3.741657387 + 7

Combine like terms: -3.741657387 + 7 = 3.258342613
x = 3.258342613

Simplifying
x = 3.258342613


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.741657387, 3.258342613}
Solution
x = {10.741657387, 3.258342613}

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