0=-x^2+6x-2

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


Simplifying
0 = -1x2 + 6x + -2

Reorder the terms:
0 = -2 + 6x + -1x2

Solving
0 = -2 + 6x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + -6x + x2 = -2 + 6x + -1x2 + 2 + -6x + x2

Reorder the terms:
2 + -6x + x2 = -2 + 2 + 6x + -6x + -1x2 + x2

Combine like terms: -2 + 2 = 0
2 + -6x + x2 = 0 + 6x + -6x + -1x2 + x2
2 + -6x + x2 = 6x + -6x + -1x2 + x2

Combine like terms: 6x + -6x = 0
2 + -6x + x2 = 0 + -1x2 + x2
2 + -6x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
2 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -6x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -6x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -6x + x2 = 0 + -2
-6x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-6x + x2 = -2

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 = -2 + 9

Reorder the terms:
9 + -6x + x2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + -6x + x2 = 7

Factor a perfect square on the left side:
(x + -3)(x + -3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -3) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + -3 = 2.645751311 Simplifying x + -3 = 2.645751311 Reorder the terms: -3 + x = 2.645751311 Solving -3 + x = 2.645751311 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 = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.645751311 + 3 x = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 x = 5.645751311 Simplifying x = 5.645751311

Subproblem 2

x + -3 = -2.645751311 Simplifying x + -3 = -2.645751311 Reorder the terms: -3 + x = -2.645751311 Solving -3 + x = -2.645751311 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 = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.645751311 + 3 x = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 x = 0.354248689 Simplifying x = 0.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.645751311, 0.354248689}

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