x^2-6.4625x+10.24=0

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Solution for x^2-6.4625x+10.24=0 equation: 


Simplifying
x2 + -6.4625x + 10.24 = 0

Reorder the terms:
10.24 + -6.4625x + x2 = 0

Solving
10.24 + -6.4625x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-10.24' to each side of the equation.
10.24 + -6.4625x + -10.24 + x2 = 0 + -10.24

Reorder the terms:
10.24 + -10.24 + -6.4625x + x2 = 0 + -10.24

Combine like terms: 10.24 + -10.24 = 0.00
0.00 + -6.4625x + x2 = 0 + -10.24
-6.4625x + x2 = 0 + -10.24

Combine like terms: 0 + -10.24 = -10.24
-6.4625x + x2 = -10.24

The x term is -6.4625x.  Take half its coefficient (-3.23125).
Square it (10.44097656) and add it to both sides.

Add '10.44097656' to each side of the equation.
-6.4625x + 10.44097656 + x2 = -10.24 + 10.44097656

Reorder the terms:
10.44097656 + -6.4625x + x2 = -10.24 + 10.44097656

Combine like terms: -10.24 + 10.44097656 = 0.20097656
10.44097656 + -6.4625x + x2 = 0.20097656

Factor a perfect square on the left side:
(x + -3.23125)(x + -3.23125) = 0.20097656

Calculate the square root of the right side: 0.448304093

Break this problem into two subproblems by setting 
(x + -3.23125) equal to 0.448304093 and -0.448304093.


Subproblem 1
x + -3.23125 = 0.448304093

Simplifying
x + -3.23125 = 0.448304093

Reorder the terms:
-3.23125 + x = 0.448304093

Solving
-3.23125 + x = 0.448304093

Solving for variable 'x'.

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

Add '3.23125' to each side of the equation.
-3.23125 + 3.23125 + x = 0.448304093 + 3.23125

Combine like terms: -3.23125 + 3.23125 = 0.00000
0.00000 + x = 0.448304093 + 3.23125
x = 0.448304093 + 3.23125

Combine like terms: 0.448304093 + 3.23125 = 3.679554093
x = 3.679554093

Simplifying
x = 3.679554093


Subproblem 2
x + -3.23125 = -0.448304093

Simplifying
x + -3.23125 = -0.448304093

Reorder the terms:
-3.23125 + x = -0.448304093

Solving
-3.23125 + x = -0.448304093

Solving for variable 'x'.

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

Add '3.23125' to each side of the equation.
-3.23125 + 3.23125 + x = -0.448304093 + 3.23125

Combine like terms: -3.23125 + 3.23125 = 0.00000
0.00000 + x = -0.448304093 + 3.23125
x = -0.448304093 + 3.23125

Combine like terms: -0.448304093 + 3.23125 = 2.782945907
x = 2.782945907

Simplifying
x = 2.782945907


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.679554093, 2.782945907}

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