x^2-6x-1=30

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Solution for x^2-6x-1=30 equation:


Simplifying
x2 + -6x + -1 = 30

Reorder the terms:
-1 + -6x + x2 = 30

Solving
-1 + -6x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
-1 + -30 + -6x + x2 = 30 + -30

Combine like terms: -1 + -30 = -31
-31 + -6x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-31 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -6x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + -6x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -6x + x2 = 0 + 31
-6x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
-6x + x2 = 31

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 = 31 + 9

Reorder the terms:
9 + -6x + x2 = 31 + 9

Combine like terms: 31 + 9 = 40
9 + -6x + x2 = 40

Factor a perfect square on the left side:
(x + -3)(x + -3) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -3) equal to 6.32455532 and -6.32455532.

Subproblem 1

x + -3 = 6.32455532 Simplifying x + -3 = 6.32455532 Reorder the terms: -3 + x = 6.32455532 Solving -3 + x = 6.32455532 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 = 6.32455532 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.32455532 + 3 x = 6.32455532 + 3 Combine like terms: 6.32455532 + 3 = 9.32455532 x = 9.32455532 Simplifying x = 9.32455532

Subproblem 2

x + -3 = -6.32455532 Simplifying x + -3 = -6.32455532 Reorder the terms: -3 + x = -6.32455532 Solving -3 + x = -6.32455532 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 = -6.32455532 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.32455532 + 3 x = -6.32455532 + 3 Combine like terms: -6.32455532 + 3 = -3.32455532 x = -3.32455532 Simplifying x = -3.32455532

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.32455532, -3.32455532}

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