6x^2+49x+47=0

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Solution for 6x^2+49x+47=0 equation: 


Simplifying
6x2 + 49x + 47 = 0

Reorder the terms:
47 + 49x + 6x2 = 0

Solving
47 + 49x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
7.833333333 + 8.166666667x + x2 = 0

Move the constant term to the right:

Add '-7.833333333' to each side of the equation.
7.833333333 + 8.166666667x + -7.833333333 + x2 = 0 + -7.833333333

Reorder the terms:
7.833333333 + -7.833333333 + 8.166666667x + x2 = 0 + -7.833333333

Combine like terms: 7.833333333 + -7.833333333 = 0.000000000
0.000000000 + 8.166666667x + x2 = 0 + -7.833333333
8.166666667x + x2 = 0 + -7.833333333

Combine like terms: 0 + -7.833333333 = -7.833333333
8.166666667x + x2 = -7.833333333

The x term is 8.166666667x.  Take half its coefficient (4.083333334).
Square it (16.67361112) and add it to both sides.

Add '16.67361112' to each side of the equation.
8.166666667x + 16.67361112 + x2 = -7.833333333 + 16.67361112

Reorder the terms:
16.67361112 + 8.166666667x + x2 = -7.833333333 + 16.67361112

Combine like terms: -7.833333333 + 16.67361112 = 8.840277787
16.67361112 + 8.166666667x + x2 = 8.840277787

Factor a perfect square on the left side:
(x + 4.083333334)(x + 4.083333334) = 8.840277787

Calculate the square root of the right side: 2.973260464

Break this problem into two subproblems by setting 
(x + 4.083333334) equal to 2.973260464 and -2.973260464.


Subproblem 1
x + 4.083333334 = 2.973260464

Simplifying
x + 4.083333334 = 2.973260464

Reorder the terms:
4.083333334 + x = 2.973260464

Solving
4.083333334 + x = 2.973260464

Solving for variable 'x'.

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

Add '-4.083333334' to each side of the equation.
4.083333334 + -4.083333334 + x = 2.973260464 + -4.083333334

Combine like terms: 4.083333334 + -4.083333334 = 0.000000000
0.000000000 + x = 2.973260464 + -4.083333334
x = 2.973260464 + -4.083333334

Combine like terms: 2.973260464 + -4.083333334 = -1.11007287
x = -1.11007287

Simplifying
x = -1.11007287


Subproblem 2
x + 4.083333334 = -2.973260464

Simplifying
x + 4.083333334 = -2.973260464

Reorder the terms:
4.083333334 + x = -2.973260464

Solving
4.083333334 + x = -2.973260464

Solving for variable 'x'.

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

Add '-4.083333334' to each side of the equation.
4.083333334 + -4.083333334 + x = -2.973260464 + -4.083333334

Combine like terms: 4.083333334 + -4.083333334 = 0.000000000
0.000000000 + x = -2.973260464 + -4.083333334
x = -2.973260464 + -4.083333334

Combine like terms: -2.973260464 + -4.083333334 = -7.056593798
x = -7.056593798

Simplifying
x = -7.056593798


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.11007287, -7.056593798}

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