X^2-5X+6.25=9.75

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Solution for X^2-5X+6.25=9.75 equation: 


Simplifying
X2 + -5X + 6.25 = 9.75

Reorder the terms:
6.25 + -5X + X2 = 9.75

Solving
6.25 + -5X + X2 = 9.75

Solving for variable 'X'.

Reorder the terms:
6.25 + -9.75 + -5X + X2 = 9.75 + -9.75

Combine like terms: 6.25 + -9.75 = -3.5
-3.5 + -5X + X2 = 9.75 + -9.75

Combine like terms: 9.75 + -9.75 = 0.00
-3.5 + -5X + X2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -5X + 3.5 + X2 = 0.00 + 3.5

Reorder the terms:
-3.5 + 3.5 + -5X + X2 = 0.00 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -5X + X2 = 0.00 + 3.5
-5X + X2 = 0.00 + 3.5

Combine like terms: 0.00 + 3.5 = 3.5
-5X + X2 = 3.5

The X term is -5X.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5X + 6.25 + X2 = 3.5 + 6.25

Reorder the terms:
6.25 + -5X + X2 = 3.5 + 6.25

Combine like terms: 3.5 + 6.25 = 9.75
6.25 + -5X + X2 = 9.75

Factor a perfect square on the left side:
(X + -2.5)(X + -2.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(X + -2.5) equal to 3.122498999 and -3.122498999.


Subproblem 1
X + -2.5 = 3.122498999

Simplifying
X + -2.5 = 3.122498999

Reorder the terms:
-2.5 + X = 3.122498999

Solving
-2.5 + X = 3.122498999

Solving for variable 'X'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + X = 3.122498999 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + X = 3.122498999 + 2.5
X = 3.122498999 + 2.5

Combine like terms: 3.122498999 + 2.5 = 5.622498999
X = 5.622498999

Simplifying
X = 5.622498999


Subproblem 2
X + -2.5 = -3.122498999

Simplifying
X + -2.5 = -3.122498999

Reorder the terms:
-2.5 + X = -3.122498999

Solving
-2.5 + X = -3.122498999

Solving for variable 'X'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + X = -3.122498999 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + X = -3.122498999 + 2.5
X = -3.122498999 + 2.5

Combine like terms: -3.122498999 + 2.5 = -0.622498999
X = -0.622498999

Simplifying
X = -0.622498999


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {5.622498999, -0.622498999}

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