-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 = 24.506944453
16.67361112 + -8.166666667x + x2 = 24.506944453

Factor a perfect square on the left side:
(x + -4.083333334)(x + -4.083333334) = 24.506944453

Calculate the square root of the right side: 4.950448914

Break this problem into two subproblems by setting 
(x + -4.083333334) equal to 4.950448914 and -4.950448914.


Subproblem 1
x + -4.083333334 = 4.950448914

Simplifying
x + -4.083333334 = 4.950448914

Reorder the terms:
-4.083333334 + x = 4.950448914

Solving
-4.083333334 + x = 4.950448914

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 = 4.950448914 + 4.083333334

Combine like terms: -4.083333334 + 4.083333334 = 0.000000000
0.000000000 + x = 4.950448914 + 4.083333334
x = 4.950448914 + 4.083333334

Combine like terms: 4.950448914 + 4.083333334 = 9.033782248
x = 9.033782248

Simplifying
x = 9.033782248


Subproblem 2
x + -4.083333334 = -4.950448914

Simplifying
x + -4.083333334 = -4.950448914

Reorder the terms:
-4.083333334 + x = -4.950448914

Solving
-4.083333334 + x = -4.950448914

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 = -4.950448914 + 4.083333334

Combine like terms: -4.083333334 + 4.083333334 = 0.000000000
0.000000000 + x = -4.950448914 + 4.083333334
x = -4.950448914 + 4.083333334

Combine like terms: -4.950448914 + 4.083333334 = -0.86711558
x = -0.86711558

Simplifying
x = -0.86711558


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.033782248, -0.86711558}

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