6x^2+17x-64=0

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Solution for 6x^2+17x-64=0 equation:


Simplifying
6x2 + 17x + -64 = 0

Reorder the terms:
-64 + 17x + 6x2 = 0

Solving
-64 + 17x + 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'.
-10.66666667 + 2.833333333x + x2 = 0

Move the constant term to the right:

Add '10.66666667' to each side of the equation.
-10.66666667 + 2.833333333x + 10.66666667 + x2 = 0 + 10.66666667

Reorder the terms:
-10.66666667 + 10.66666667 + 2.833333333x + x2 = 0 + 10.66666667

Combine like terms: -10.66666667 + 10.66666667 = 0.00000000
0.00000000 + 2.833333333x + x2 = 0 + 10.66666667
2.833333333x + x2 = 0 + 10.66666667

Combine like terms: 0 + 10.66666667 = 10.66666667
2.833333333x + x2 = 10.66666667

The x term is 2.833333333x.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333x + 2.006944445 + x2 = 10.66666667 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333x + x2 = 10.66666667 + 2.006944445

Combine like terms: 10.66666667 + 2.006944445 = 12.673611115
2.006944445 + 2.833333333x + x2 = 12.673611115

Factor a perfect square on the left side:
(x + 1.416666667)(x + 1.416666667) = 12.673611115

Calculate the square root of the right side: 3.560001561

Break this problem into two subproblems by setting 
(x + 1.416666667) equal to 3.560001561 and -3.560001561.

Subproblem 1

x + 1.416666667 = 3.560001561 Simplifying x + 1.416666667 = 3.560001561 Reorder the terms: 1.416666667 + x = 3.560001561 Solving 1.416666667 + x = 3.560001561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = 3.560001561 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = 3.560001561 + -1.416666667 x = 3.560001561 + -1.416666667 Combine like terms: 3.560001561 + -1.416666667 = 2.143334894 x = 2.143334894 Simplifying x = 2.143334894

Subproblem 2

x + 1.416666667 = -3.560001561 Simplifying x + 1.416666667 = -3.560001561 Reorder the terms: 1.416666667 + x = -3.560001561 Solving 1.416666667 + x = -3.560001561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = -3.560001561 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = -3.560001561 + -1.416666667 x = -3.560001561 + -1.416666667 Combine like terms: -3.560001561 + -1.416666667 = -4.976668228 x = -4.976668228 Simplifying x = -4.976668228

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.143334894, -4.976668228}

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