9x^2-44x+25=0

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Solution for 9x^2-44x+25=0 equation: 


Simplifying
9x2 + -44x + 25 = 0

Reorder the terms:
25 + -44x + 9x2 = 0

Solving
25 + -44x + 9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
2.777777778 + -4.888888889x + x2 = 0

Move the constant term to the right:

Add '-2.777777778' to each side of the equation.
2.777777778 + -4.888888889x + -2.777777778 + x2 = 0 + -2.777777778

Reorder the terms:
2.777777778 + -2.777777778 + -4.888888889x + x2 = 0 + -2.777777778

Combine like terms: 2.777777778 + -2.777777778 = 0.000000000
0.000000000 + -4.888888889x + x2 = 0 + -2.777777778
-4.888888889x + x2 = 0 + -2.777777778

Combine like terms: 0 + -2.777777778 = -2.777777778
-4.888888889x + x2 = -2.777777778

The x term is -4.888888889x.  Take half its coefficient (-2.444444445).
Square it (5.975308645) and add it to both sides.

Add '5.975308645' to each side of the equation.
-4.888888889x + 5.975308645 + x2 = -2.777777778 + 5.975308645

Reorder the terms:
5.975308645 + -4.888888889x + x2 = -2.777777778 + 5.975308645

Combine like terms: -2.777777778 + 5.975308645 = 3.197530867
5.975308645 + -4.888888889x + x2 = 3.197530867

Factor a perfect square on the left side:
(x + -2.444444445)(x + -2.444444445) = 3.197530867

Calculate the square root of the right side: 1.788164105

Break this problem into two subproblems by setting 
(x + -2.444444445) equal to 1.788164105 and -1.788164105.


Subproblem 1
x + -2.444444445 = 1.788164105

Simplifying
x + -2.444444445 = 1.788164105

Reorder the terms:
-2.444444445 + x = 1.788164105

Solving
-2.444444445 + x = 1.788164105

Solving for variable 'x'.

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

Add '2.444444445' to each side of the equation.
-2.444444445 + 2.444444445 + x = 1.788164105 + 2.444444445

Combine like terms: -2.444444445 + 2.444444445 = 0.000000000
0.000000000 + x = 1.788164105 + 2.444444445
x = 1.788164105 + 2.444444445

Combine like terms: 1.788164105 + 2.444444445 = 4.23260855
x = 4.23260855

Simplifying
x = 4.23260855


Subproblem 2
x + -2.444444445 = -1.788164105

Simplifying
x + -2.444444445 = -1.788164105

Reorder the terms:
-2.444444445 + x = -1.788164105

Solving
-2.444444445 + x = -1.788164105

Solving for variable 'x'.

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

Add '2.444444445' to each side of the equation.
-2.444444445 + 2.444444445 + x = -1.788164105 + 2.444444445

Combine like terms: -2.444444445 + 2.444444445 = 0.000000000
0.000000000 + x = -1.788164105 + 2.444444445
x = -1.788164105 + 2.444444445

Combine like terms: -1.788164105 + 2.444444445 = 0.65628034
x = 0.65628034

Simplifying
x = 0.65628034


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.23260855, 0.65628034}

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