6x^2-49x+4=0

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Solution for 6x^2-49x+4=0 equation: 


Simplifying
6x2 + -49x + 4 = 0

Reorder the terms:
4 + -49x + 6x2 = 0

Solving
4 + -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'.
0.6666666667 + -8.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -8.166666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -8.166666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -8.166666667x + x2 = 0 + -0.6666666667
-8.166666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-8.166666667x + x2 = -0.6666666667

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 = -0.6666666667 + 16.67361112

Reorder the terms:
16.67361112 + -8.166666667x + x2 = -0.6666666667 + 16.67361112

Combine like terms: -0.6666666667 + 16.67361112 = 16.0069444533
16.67361112 + -8.166666667x + x2 = 16.0069444533

Factor a perfect square on the left side:
(x + -4.083333334)(x + -4.083333334) = 16.0069444533

Calculate the square root of the right side: 4.000867962

Break this problem into two subproblems by setting 
(x + -4.083333334) equal to 4.000867962 and -4.000867962.


Subproblem 1
x + -4.083333334 = 4.000867962

Simplifying
x + -4.083333334 = 4.000867962

Reorder the terms:
-4.083333334 + x = 4.000867962

Solving
-4.083333334 + x = 4.000867962

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 = 4.000867962 + 4.083333334

Combine like terms: -4.083333334 + 4.083333334 = 0.000000000
0.000000000 + x = 4.000867962 + 4.083333334
x = 4.000867962 + 4.083333334

Combine like terms: 4.000867962 + 4.083333334 = 8.084201296
x = 8.084201296

Simplifying
x = 8.084201296


Subproblem 2
x + -4.083333334 = -4.000867962

Simplifying
x + -4.083333334 = -4.000867962

Reorder the terms:
-4.083333334 + x = -4.000867962

Solving
-4.083333334 + x = -4.000867962

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 = -4.000867962 + 4.083333334

Combine like terms: -4.083333334 + 4.083333334 = 0.000000000
0.000000000 + x = -4.000867962 + 4.083333334
x = -4.000867962 + 4.083333334

Combine like terms: -4.000867962 + 4.083333334 = 0.082465372
x = 0.082465372

Simplifying
x = 0.082465372


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.084201296, 0.082465372}

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