3x^2+42x+49=0

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Solution for 3x^2+42x+49=0 equation: 


Simplifying
3x2 + 42x + 49 = 0

Reorder the terms:
49 + 42x + 3x2 = 0

Solving
49 + 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'.
16.33333333 + 14x + x2 = 0

Move the constant term to the right:

Add '-16.33333333' to each side of the equation.
16.33333333 + 14x + -16.33333333 + x2 = 0 + -16.33333333

Reorder the terms:
16.33333333 + -16.33333333 + 14x + x2 = 0 + -16.33333333

Combine like terms: 16.33333333 + -16.33333333 = 0.00000000
0.00000000 + 14x + x2 = 0 + -16.33333333
14x + x2 = 0 + -16.33333333

Combine like terms: 0 + -16.33333333 = -16.33333333
14x + x2 = -16.33333333

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 = -16.33333333 + 49

Reorder the terms:
49 + 14x + x2 = -16.33333333 + 49

Combine like terms: -16.33333333 + 49 = 32.66666667
49 + 14x + x2 = 32.66666667

Factor a perfect square on the left side:
(x + 7)(x + 7) = 32.66666667

Calculate the square root of the right side: 5.715476067

Break this problem into two subproblems by setting 
(x + 7) equal to 5.715476067 and -5.715476067.


Subproblem 1
x + 7 = 5.715476067

Simplifying
x + 7 = 5.715476067

Reorder the terms:
7 + x = 5.715476067

Solving
7 + x = 5.715476067

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 = 5.715476067 + -7

Combine like terms: 7 + -7 = 0
0 + x = 5.715476067 + -7
x = 5.715476067 + -7

Combine like terms: 5.715476067 + -7 = -1.284523933
x = -1.284523933

Simplifying
x = -1.284523933


Subproblem 2
x + 7 = -5.715476067

Simplifying
x + 7 = -5.715476067

Reorder the terms:
7 + x = -5.715476067

Solving
7 + x = -5.715476067

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 = -5.715476067 + -7

Combine like terms: 7 + -7 = 0
0 + x = -5.715476067 + -7
x = -5.715476067 + -7

Combine like terms: -5.715476067 + -7 = -12.715476067
x = -12.715476067

Simplifying
x = -12.715476067


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.284523933, -12.715476067}

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