0=-x^2-6x+1

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


Simplifying
0 = -1x2 + -6x + 1

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

Solving
0 = 1 + -6x + -1x2

Solving for variable 'x'.

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

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

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

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

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

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 = 0.16227766 x = 0.16227766 Simplifying x = 0.16227766

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 = -6.16227766 x = -6.16227766 Simplifying x = -6.16227766

Solution

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

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