x^2-6x-1=0

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Solution for x^2-6x-1=0 equation:


Simplifying
x2 + -6x + -1 = 0

Reorder the terms:
-1 + -6x + x2 = 0

Solving
-1 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -6x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6x + x2 = 0 + 1
-6x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-6x + x2 = 1

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 = 1 + 9

Reorder the terms:
9 + -6x + x2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + -6x + x2 = 10

Factor a perfect square on the left side:
(x + -3)(x + -3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -3) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + -3 = 3.16227766 Simplifying x + -3 = 3.16227766 Reorder the terms: -3 + x = 3.16227766 Solving -3 + x = 3.16227766 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 = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.16227766 + 3 x = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 x = 6.16227766 Simplifying x = 6.16227766

Subproblem 2

x + -3 = -3.16227766 Simplifying x + -3 = -3.16227766 Reorder the terms: -3 + x = -3.16227766 Solving -3 + x = -3.16227766 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 = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.16227766 + 3 x = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 x = -0.16227766 Simplifying x = -0.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.16227766, -0.16227766}

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