(m^2-m-2.5m+2.5)=0

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Solution for (m^2-m-2.5m+2.5)=0 equation: 


Simplifying
(m2 + -1m + -2.5m + 2.5) = 0

Reorder the terms:
(2.5 + -1m + -2.5m + m2) = 0

Combine like terms: -1m + -2.5m = -3.5m
(2.5 + -3.5m + m2) = 0

Remove parenthesis around (2.5 + -3.5m + m2)
2.5 + -3.5m + m2 = 0

Solving
2.5 + -3.5m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -3.5m + -2.5 + m2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -3.5m + m2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -3.5m + m2 = 0 + -2.5
-3.5m + m2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-3.5m + m2 = -2.5

The m term is -3.5m.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5m + 3.0625 + m2 = -2.5 + 3.0625

Reorder the terms:
3.0625 + -3.5m + m2 = -2.5 + 3.0625

Combine like terms: -2.5 + 3.0625 = 0.5625
3.0625 + -3.5m + m2 = 0.5625

Factor a perfect square on the left side:
(m + -1.75)(m + -1.75) = 0.5625

Calculate the square root of the right side: 0.75

Break this problem into two subproblems by setting 
(m + -1.75) equal to 0.75 and -0.75.


Subproblem 1
m + -1.75 = 0.75

Simplifying
m + -1.75 = 0.75

Reorder the terms:
-1.75 + m = 0.75

Solving
-1.75 + m = 0.75

Solving for variable 'm'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + m = 0.75 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + m = 0.75 + 1.75
m = 0.75 + 1.75

Combine like terms: 0.75 + 1.75 = 2.5
m = 2.5

Simplifying
m = 2.5


Subproblem 2
m + -1.75 = -0.75

Simplifying
m + -1.75 = -0.75

Reorder the terms:
-1.75 + m = -0.75

Solving
-1.75 + m = -0.75

Solving for variable 'm'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + m = -0.75 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + m = -0.75 + 1.75
m = -0.75 + 1.75

Combine like terms: -0.75 + 1.75 = 1
m = 1

Simplifying
m = 1


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.5, 1}

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