x^2-22x+.85=0

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Solution for x^2-22x+.85=0 equation:


Simplifying
x2 + -22x + 0.85 = 0

Reorder the terms:
0.85 + -22x + x2 = 0

Solving
0.85 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.85' to each side of the equation.
0.85 + -22x + -0.85 + x2 = 0 + -0.85

Reorder the terms:
0.85 + -0.85 + -22x + x2 = 0 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + -22x + x2 = 0 + -0.85
-22x + x2 = 0 + -0.85

Combine like terms: 0 + -0.85 = -0.85
-22x + x2 = -0.85

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = -0.85 + 121

Reorder the terms:
121 + -22x + x2 = -0.85 + 121

Combine like terms: -0.85 + 121 = 120.15
121 + -22x + x2 = 120.15

Factor a perfect square on the left side:
(x + -11)(x + -11) = 120.15

Calculate the square root of the right side: 10.961295544

Break this problem into two subproblems by setting 
(x + -11) equal to 10.961295544 and -10.961295544.

Subproblem 1

x + -11 = 10.961295544 Simplifying x + -11 = 10.961295544 Reorder the terms: -11 + x = 10.961295544 Solving -11 + x = 10.961295544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 10.961295544 + 11 Combine like terms: -11 + 11 = 0 0 + x = 10.961295544 + 11 x = 10.961295544 + 11 Combine like terms: 10.961295544 + 11 = 21.961295544 x = 21.961295544 Simplifying x = 21.961295544

Subproblem 2

x + -11 = -10.961295544 Simplifying x + -11 = -10.961295544 Reorder the terms: -11 + x = -10.961295544 Solving -11 + x = -10.961295544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -10.961295544 + 11 Combine like terms: -11 + 11 = 0 0 + x = -10.961295544 + 11 x = -10.961295544 + 11 Combine like terms: -10.961295544 + 11 = 0.038704456 x = 0.038704456 Simplifying x = 0.038704456

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.961295544, 0.038704456}

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