x^2+6x-65=0

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Solution for x^2+6x-65=0 equation:


Simplifying
x2 + 6x + -65 = 0

Reorder the terms:
-65 + 6x + x2 = 0

Solving
-65 + 6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + 6x + 65 + x2 = 0 + 65

Reorder the terms:
-65 + 65 + 6x + x2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + 6x + x2 = 0 + 65
6x + x2 = 0 + 65

Combine like terms: 0 + 65 = 65
6x + x2 = 65

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 65 + 9

Reorder the terms:
9 + 6x + x2 = 65 + 9

Combine like terms: 65 + 9 = 74
9 + 6x + x2 = 74

Factor a perfect square on the left side:
(x + 3)(x + 3) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(x + 3) equal to 8.602325267 and -8.602325267.

Subproblem 1

x + 3 = 8.602325267 Simplifying x + 3 = 8.602325267 Reorder the terms: 3 + x = 8.602325267 Solving 3 + x = 8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 8.602325267 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.602325267 + -3 x = 8.602325267 + -3 Combine like terms: 8.602325267 + -3 = 5.602325267 x = 5.602325267 Simplifying x = 5.602325267

Subproblem 2

x + 3 = -8.602325267 Simplifying x + 3 = -8.602325267 Reorder the terms: 3 + x = -8.602325267 Solving 3 + x = -8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -8.602325267 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.602325267 + -3 x = -8.602325267 + -3 Combine like terms: -8.602325267 + -3 = -11.602325267 x = -11.602325267 Simplifying x = -11.602325267

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.602325267, -11.602325267}

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