x^2-6x+1.8855=0

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Solution for x^2-6x+1.8855=0 equation:


Simplifying
x2 + -6x + 1.8855 = 0

Reorder the terms:
1.8855 + -6x + x2 = 0

Solving
1.8855 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.8855' to each side of the equation.
1.8855 + -6x + -1.8855 + x2 = 0 + -1.8855

Reorder the terms:
1.8855 + -1.8855 + -6x + x2 = 0 + -1.8855

Combine like terms: 1.8855 + -1.8855 = 0.0000
0.0000 + -6x + x2 = 0 + -1.8855
-6x + x2 = 0 + -1.8855

Combine like terms: 0 + -1.8855 = -1.8855
-6x + x2 = -1.8855

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 = -1.8855 + 9

Reorder the terms:
9 + -6x + x2 = -1.8855 + 9

Combine like terms: -1.8855 + 9 = 7.1145
9 + -6x + x2 = 7.1145

Factor a perfect square on the left side:
(x + -3)(x + -3) = 7.1145

Calculate the square root of the right side: 2.667302008

Break this problem into two subproblems by setting 
(x + -3) equal to 2.667302008 and -2.667302008.

Subproblem 1

x + -3 = 2.667302008 Simplifying x + -3 = 2.667302008 Reorder the terms: -3 + x = 2.667302008 Solving -3 + x = 2.667302008 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 = 2.667302008 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.667302008 + 3 x = 2.667302008 + 3 Combine like terms: 2.667302008 + 3 = 5.667302008 x = 5.667302008 Simplifying x = 5.667302008

Subproblem 2

x + -3 = -2.667302008 Simplifying x + -3 = -2.667302008 Reorder the terms: -3 + x = -2.667302008 Solving -3 + x = -2.667302008 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 = -2.667302008 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.667302008 + 3 x = -2.667302008 + 3 Combine like terms: -2.667302008 + 3 = 0.332697992 x = 0.332697992 Simplifying x = 0.332697992

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.667302008, 0.332697992}

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