6x^2-35x-36=0

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Solution for 6x^2-35x-36=0 equation:


Simplifying
6x2 + -35x + -36 = 0

Reorder the terms:
-36 + -35x + 6x2 = 0

Solving
-36 + -35x + 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'.
-6 + -5.833333333x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -5.833333333x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -5.833333333x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5.833333333x + x2 = 0 + 6
-5.833333333x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-5.833333333x + x2 = 6

The x term is -5.833333333x.  Take half its coefficient (-2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
-5.833333333x + 8.506944446 + x2 = 6 + 8.506944446

Reorder the terms:
8.506944446 + -5.833333333x + x2 = 6 + 8.506944446

Combine like terms: 6 + 8.506944446 = 14.506944446
8.506944446 + -5.833333333x + x2 = 14.506944446

Factor a perfect square on the left side:
(x + -2.916666667)(x + -2.916666667) = 14.506944446

Calculate the square root of the right side: 3.808798294

Break this problem into two subproblems by setting 
(x + -2.916666667) equal to 3.808798294 and -3.808798294.

Subproblem 1

x + -2.916666667 = 3.808798294 Simplifying x + -2.916666667 = 3.808798294 Reorder the terms: -2.916666667 + x = 3.808798294 Solving -2.916666667 + x = 3.808798294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = 3.808798294 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = 3.808798294 + 2.916666667 x = 3.808798294 + 2.916666667 Combine like terms: 3.808798294 + 2.916666667 = 6.725464961 x = 6.725464961 Simplifying x = 6.725464961

Subproblem 2

x + -2.916666667 = -3.808798294 Simplifying x + -2.916666667 = -3.808798294 Reorder the terms: -2.916666667 + x = -3.808798294 Solving -2.916666667 + x = -3.808798294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = -3.808798294 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = -3.808798294 + 2.916666667 x = -3.808798294 + 2.916666667 Combine like terms: -3.808798294 + 2.916666667 = -0.892131627 x = -0.892131627 Simplifying x = -0.892131627

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.725464961, -0.892131627}

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