3x^2-42x+142=0

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Solution for 3x^2-42x+142=0 equation: 


Simplifying
3x2 + -42x + 142 = 0

Reorder the terms:
142 + -42x + 3x2 = 0

Solving
142 + -42x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
47.33333333 + -14x + x2 = 0

Move the constant term to the right:

Add '-47.33333333' to each side of the equation.
47.33333333 + -14x + -47.33333333 + x2 = 0 + -47.33333333

Reorder the terms:
47.33333333 + -47.33333333 + -14x + x2 = 0 + -47.33333333

Combine like terms: 47.33333333 + -47.33333333 = 0.00000000
0.00000000 + -14x + x2 = 0 + -47.33333333
-14x + x2 = 0 + -47.33333333

Combine like terms: 0 + -47.33333333 = -47.33333333
-14x + x2 = -47.33333333

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 = -47.33333333 + 49

Reorder the terms:
49 + -14x + x2 = -47.33333333 + 49

Combine like terms: -47.33333333 + 49 = 1.66666667
49 + -14x + x2 = 1.66666667

Factor a perfect square on the left side:
(x + -7)(x + -7) = 1.66666667

Calculate the square root of the right side: 1.29099445

Break this problem into two subproblems by setting 
(x + -7) equal to 1.29099445 and -1.29099445.


Subproblem 1
x + -7 = 1.29099445

Simplifying
x + -7 = 1.29099445

Reorder the terms:
-7 + x = 1.29099445

Solving
-7 + x = 1.29099445

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 = 1.29099445 + 7

Combine like terms: -7 + 7 = 0
0 + x = 1.29099445 + 7
x = 1.29099445 + 7

Combine like terms: 1.29099445 + 7 = 8.29099445
x = 8.29099445

Simplifying
x = 8.29099445


Subproblem 2
x + -7 = -1.29099445

Simplifying
x + -7 = -1.29099445

Reorder the terms:
-7 + x = -1.29099445

Solving
-7 + x = -1.29099445

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 = -1.29099445 + 7

Combine like terms: -7 + 7 = 0
0 + x = -1.29099445 + 7
x = -1.29099445 + 7

Combine like terms: -1.29099445 + 7 = 5.70900555
x = 5.70900555

Simplifying
x = 5.70900555


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.29099445, 5.70900555}

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