x^2-8.6x=-17.68

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Solution for x^2-8.6x=-17.68 equation: 


Simplifying
x2 + -8.6x = -17.68

Reorder the terms:
-8.6x + x2 = -17.68

Solving
-8.6x + x2 = -17.68

Solving for variable 'x'.

Reorder the terms:
17.68 + -8.6x + x2 = -17.68 + 17.68

Combine like terms: -17.68 + 17.68 = 0.00
17.68 + -8.6x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-17.68' to each side of the equation.
17.68 + -8.6x + -17.68 + x2 = 0.00 + -17.68

Reorder the terms:
17.68 + -17.68 + -8.6x + x2 = 0.00 + -17.68

Combine like terms: 17.68 + -17.68 = 0.00
0.00 + -8.6x + x2 = 0.00 + -17.68
-8.6x + x2 = 0.00 + -17.68

Combine like terms: 0.00 + -17.68 = -17.68
-8.6x + x2 = -17.68

The x term is -8.6x.  Take half its coefficient (-4.3).
Square it (18.49) and add it to both sides.

Add '18.49' to each side of the equation.
-8.6x + 18.49 + x2 = -17.68 + 18.49

Reorder the terms:
18.49 + -8.6x + x2 = -17.68 + 18.49

Combine like terms: -17.68 + 18.49 = 0.81
18.49 + -8.6x + x2 = 0.81

Factor a perfect square on the left side:
(x + -4.3)(x + -4.3) = 0.81

Calculate the square root of the right side: 0.9

Break this problem into two subproblems by setting 
(x + -4.3) equal to 0.9 and -0.9.


Subproblem 1
x + -4.3 = 0.9

Simplifying
x + -4.3 = 0.9

Reorder the terms:
-4.3 + x = 0.9

Solving
-4.3 + x = 0.9

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.3' to each side of the equation.
-4.3 + 4.3 + x = 0.9 + 4.3

Combine like terms: -4.3 + 4.3 = 0.0
0.0 + x = 0.9 + 4.3
x = 0.9 + 4.3

Combine like terms: 0.9 + 4.3 = 5.2
x = 5.2

Simplifying
x = 5.2


Subproblem 2
x + -4.3 = -0.9

Simplifying
x + -4.3 = -0.9

Reorder the terms:
-4.3 + x = -0.9

Solving
-4.3 + x = -0.9

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.3' to each side of the equation.
-4.3 + 4.3 + x = -0.9 + 4.3

Combine like terms: -4.3 + 4.3 = 0.0
0.0 + x = -0.9 + 4.3
x = -0.9 + 4.3

Combine like terms: -0.9 + 4.3 = 3.4
x = 3.4

Simplifying
x = 3.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.2, 3.4}

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