3x^2+46x+49=0

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Solution for 3x^2+46x+49=0 equation: 


Simplifying
3x2 + 46x + 49 = 0

Reorder the terms:
49 + 46x + 3x2 = 0

Solving
49 + 46x + 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 + 15.33333333x + x2 = 0

Move the constant term to the right:

Add '-16.33333333' to each side of the equation.
16.33333333 + 15.33333333x + -16.33333333 + x2 = 0 + -16.33333333

Reorder the terms:
16.33333333 + -16.33333333 + 15.33333333x + x2 = 0 + -16.33333333

Combine like terms: 16.33333333 + -16.33333333 = 0.00000000
0.00000000 + 15.33333333x + x2 = 0 + -16.33333333
15.33333333x + x2 = 0 + -16.33333333

Combine like terms: 0 + -16.33333333 = -16.33333333
15.33333333x + x2 = -16.33333333

The x term is 15.33333333x.  Take half its coefficient (7.666666665).
Square it (58.77777775) and add it to both sides.

Add '58.77777775' to each side of the equation.
15.33333333x + 58.77777775 + x2 = -16.33333333 + 58.77777775

Reorder the terms:
58.77777775 + 15.33333333x + x2 = -16.33333333 + 58.77777775

Combine like terms: -16.33333333 + 58.77777775 = 42.44444442
58.77777775 + 15.33333333x + x2 = 42.44444442

Factor a perfect square on the left side:
(x + 7.666666665)(x + 7.666666665) = 42.44444442

Calculate the square root of the right side: 6.514940093

Break this problem into two subproblems by setting 
(x + 7.666666665) equal to 6.514940093 and -6.514940093.


Subproblem 1
x + 7.666666665 = 6.514940093

Simplifying
x + 7.666666665 = 6.514940093

Reorder the terms:
7.666666665 + x = 6.514940093

Solving
7.666666665 + x = 6.514940093

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7.666666665' to each side of the equation.
7.666666665 + -7.666666665 + x = 6.514940093 + -7.666666665

Combine like terms: 7.666666665 + -7.666666665 = 0.000000000
0.000000000 + x = 6.514940093 + -7.666666665
x = 6.514940093 + -7.666666665

Combine like terms: 6.514940093 + -7.666666665 = -1.151726572
x = -1.151726572

Simplifying
x = -1.151726572


Subproblem 2
x + 7.666666665 = -6.514940093

Simplifying
x + 7.666666665 = -6.514940093

Reorder the terms:
7.666666665 + x = -6.514940093

Solving
7.666666665 + x = -6.514940093

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7.666666665' to each side of the equation.
7.666666665 + -7.666666665 + x = -6.514940093 + -7.666666665

Combine like terms: 7.666666665 + -7.666666665 = 0.000000000
0.000000000 + x = -6.514940093 + -7.666666665
x = -6.514940093 + -7.666666665

Combine like terms: -6.514940093 + -7.666666665 = -14.181606758
x = -14.181606758

Simplifying
x = -14.181606758


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.151726572, -14.181606758}

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