x^2-8.4625x+17.64=0

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Solution for x^2-8.4625x+17.64=0 equation: 


Simplifying
x2 + -8.4625x + 17.64 = 0

Reorder the terms:
17.64 + -8.4625x + x2 = 0

Solving
17.64 + -8.4625x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-17.64' to each side of the equation.
17.64 + -8.4625x + -17.64 + x2 = 0 + -17.64

Reorder the terms:
17.64 + -17.64 + -8.4625x + x2 = 0 + -17.64

Combine like terms: 17.64 + -17.64 = 0.00
0.00 + -8.4625x + x2 = 0 + -17.64
-8.4625x + x2 = 0 + -17.64

Combine like terms: 0 + -17.64 = -17.64
-8.4625x + x2 = -17.64

The x term is -8.4625x.  Take half its coefficient (-4.23125).
Square it (17.90347656) and add it to both sides.

Add '17.90347656' to each side of the equation.
-8.4625x + 17.90347656 + x2 = -17.64 + 17.90347656

Reorder the terms:
17.90347656 + -8.4625x + x2 = -17.64 + 17.90347656

Combine like terms: -17.64 + 17.90347656 = 0.26347656
17.90347656 + -8.4625x + x2 = 0.26347656

Factor a perfect square on the left side:
(x + -4.23125)(x + -4.23125) = 0.26347656

Calculate the square root of the right side: 0.513299679

Break this problem into two subproblems by setting 
(x + -4.23125) equal to 0.513299679 and -0.513299679.


Subproblem 1
x + -4.23125 = 0.513299679

Simplifying
x + -4.23125 = 0.513299679

Reorder the terms:
-4.23125 + x = 0.513299679

Solving
-4.23125 + x = 0.513299679

Solving for variable 'x'.

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

Add '4.23125' to each side of the equation.
-4.23125 + 4.23125 + x = 0.513299679 + 4.23125

Combine like terms: -4.23125 + 4.23125 = 0.00000
0.00000 + x = 0.513299679 + 4.23125
x = 0.513299679 + 4.23125

Combine like terms: 0.513299679 + 4.23125 = 4.744549679
x = 4.744549679

Simplifying
x = 4.744549679


Subproblem 2
x + -4.23125 = -0.513299679

Simplifying
x + -4.23125 = -0.513299679

Reorder the terms:
-4.23125 + x = -0.513299679

Solving
-4.23125 + x = -0.513299679

Solving for variable 'x'.

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

Add '4.23125' to each side of the equation.
-4.23125 + 4.23125 + x = -0.513299679 + 4.23125

Combine like terms: -4.23125 + 4.23125 = 0.00000
0.00000 + x = -0.513299679 + 4.23125
x = -0.513299679 + 4.23125

Combine like terms: -0.513299679 + 4.23125 = 3.717950321
x = 3.717950321

Simplifying
x = 3.717950321


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.744549679, 3.717950321}

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