3x^2+42x+10=0

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Solution for 3x^2+42x+10=0 equation: 


Simplifying
3x2 + 42x + 10 = 0

Reorder the terms:
10 + 42x + 3x2 = 0

Solving
10 + 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'.
3.333333333 + 14x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + 14x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + 14x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + 14x + x2 = 0 + -3.333333333
14x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
14x + x2 = -3.333333333

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 = -3.333333333 + 49

Reorder the terms:
49 + 14x + x2 = -3.333333333 + 49

Combine like terms: -3.333333333 + 49 = 45.666666667
49 + 14x + x2 = 45.666666667

Factor a perfect square on the left side:
(x + 7)(x + 7) = 45.666666667

Calculate the square root of the right side: 6.757711644

Break this problem into two subproblems by setting 
(x + 7) equal to 6.757711644 and -6.757711644.


Subproblem 1
x + 7 = 6.757711644

Simplifying
x + 7 = 6.757711644

Reorder the terms:
7 + x = 6.757711644

Solving
7 + x = 6.757711644

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 = 6.757711644 + -7

Combine like terms: 7 + -7 = 0
0 + x = 6.757711644 + -7
x = 6.757711644 + -7

Combine like terms: 6.757711644 + -7 = -0.242288356
x = -0.242288356

Simplifying
x = -0.242288356


Subproblem 2
x + 7 = -6.757711644

Simplifying
x + 7 = -6.757711644

Reorder the terms:
7 + x = -6.757711644

Solving
7 + x = -6.757711644

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 = -6.757711644 + -7

Combine like terms: 7 + -7 = 0
0 + x = -6.757711644 + -7
x = -6.757711644 + -7

Combine like terms: -6.757711644 + -7 = -13.757711644
x = -13.757711644

Simplifying
x = -13.757711644


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.242288356, -13.757711644}

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