0.249x^2-4.4x+13.5=0

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Solution for 0.249x^2-4.4x+13.5=0 equation: 


Simplifying
0.249x2 + -4.4x + 13.5 = 0

Reorder the terms:
13.5 + -4.4x + 0.249x2 = 0

Solving
13.5 + -4.4x + 0.249x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.249'.
54.21686747 + -17.67068273x + x2 = 0

Move the constant term to the right:

Add '-54.21686747' to each side of the equation.
54.21686747 + -17.67068273x + -54.21686747 + x2 = 0 + -54.21686747

Reorder the terms:
54.21686747 + -54.21686747 + -17.67068273x + x2 = 0 + -54.21686747

Combine like terms: 54.21686747 + -54.21686747 = 0.00000000
0.00000000 + -17.67068273x + x2 = 0 + -54.21686747
-17.67068273x + x2 = 0 + -54.21686747

Combine like terms: 0 + -54.21686747 = -54.21686747
-17.67068273x + x2 = -54.21686747

The x term is -17.67068273x.  Take half its coefficient (-8.835341365).
Square it (78.06325704) and add it to both sides.

Add '78.06325704' to each side of the equation.
-17.67068273x + 78.06325704 + x2 = -54.21686747 + 78.06325704

Reorder the terms:
78.06325704 + -17.67068273x + x2 = -54.21686747 + 78.06325704

Combine like terms: -54.21686747 + 78.06325704 = 23.84638957
78.06325704 + -17.67068273x + x2 = 23.84638957

Factor a perfect square on the left side:
(x + -8.835341365)(x + -8.835341365) = 23.84638957

Calculate the square root of the right side: 4.88327652

Break this problem into two subproblems by setting 
(x + -8.835341365) equal to 4.88327652 and -4.88327652.


Subproblem 1
x + -8.835341365 = 4.88327652

Simplifying
x + -8.835341365 = 4.88327652

Reorder the terms:
-8.835341365 + x = 4.88327652

Solving
-8.835341365 + x = 4.88327652

Solving for variable 'x'.

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

Add '8.835341365' to each side of the equation.
-8.835341365 + 8.835341365 + x = 4.88327652 + 8.835341365

Combine like terms: -8.835341365 + 8.835341365 = 0.000000000
0.000000000 + x = 4.88327652 + 8.835341365
x = 4.88327652 + 8.835341365

Combine like terms: 4.88327652 + 8.835341365 = 13.718617885
x = 13.718617885

Simplifying
x = 13.718617885


Subproblem 2
x + -8.835341365 = -4.88327652

Simplifying
x + -8.835341365 = -4.88327652

Reorder the terms:
-8.835341365 + x = -4.88327652

Solving
-8.835341365 + x = -4.88327652

Solving for variable 'x'.

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

Add '8.835341365' to each side of the equation.
-8.835341365 + 8.835341365 + x = -4.88327652 + 8.835341365

Combine like terms: -8.835341365 + 8.835341365 = 0.000000000
0.000000000 + x = -4.88327652 + 8.835341365
x = -4.88327652 + 8.835341365

Combine like terms: -4.88327652 + 8.835341365 = 3.952064845
x = 3.952064845

Simplifying
x = 3.952064845


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.718617885, 3.952064845}

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