6x^2-49x-49=0

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


Simplifying
6x2 + -49x + -49 = 0

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

Solving
-49 + -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'.
-8.166666667 + -8.166666667x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = 8.166666667 + 16.67361112

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

Combine like terms: 8.166666667 + 16.67361112 = 24.840277787
16.67361112 + -8.166666667x + x2 = 24.840277787

Factor a perfect square on the left side:
(x + -4.083333334)(x + -4.083333334) = 24.840277787

Calculate the square root of the right side: 4.984002186

Break this problem into two subproblems by setting 
(x + -4.083333334) equal to 4.984002186 and -4.984002186.


Subproblem 1
x + -4.083333334 = 4.984002186

Simplifying
x + -4.083333334 = 4.984002186

Reorder the terms:
-4.083333334 + x = 4.984002186

Solving
-4.083333334 + x = 4.984002186

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 = 4.984002186 + 4.083333334

Combine like terms: -4.083333334 + 4.083333334 = 0.000000000
0.000000000 + x = 4.984002186 + 4.083333334
x = 4.984002186 + 4.083333334

Combine like terms: 4.984002186 + 4.083333334 = 9.06733552
x = 9.06733552

Simplifying
x = 9.06733552


Subproblem 2
x + -4.083333334 = -4.984002186

Simplifying
x + -4.083333334 = -4.984002186

Reorder the terms:
-4.083333334 + x = -4.984002186

Solving
-4.083333334 + x = -4.984002186

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 = -4.984002186 + 4.083333334

Combine like terms: -4.083333334 + 4.083333334 = 0.000000000
0.000000000 + x = -4.984002186 + 4.083333334
x = -4.984002186 + 4.083333334

Combine like terms: -4.984002186 + 4.083333334 = -0.900668852
x = -0.900668852

Simplifying
x = -0.900668852


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.06733552, -0.900668852}

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