5m-2m(m-5)=17

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Solution for 5m-2m(m-5)=17 equation: 


Simplifying
5m + -2m(m + -5) = 17

Reorder the terms:
5m + -2m(-5 + m) = 17
5m + (-5 * -2m + m * -2m) = 17
5m + (10m + -2m2) = 17

Combine like terms: 5m + 10m = 15m
15m + -2m2 = 17

Solving
15m + -2m2 = 17

Solving for variable 'm'.

Reorder the terms:
-17 + 15m + -2m2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + 15m + -2m2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
8.5 + -7.5m + m2 = 0

Move the constant term to the right:

Add '-8.5' to each side of the equation.
8.5 + -7.5m + -8.5 + m2 = 0 + -8.5

Reorder the terms:
8.5 + -8.5 + -7.5m + m2 = 0 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + -7.5m + m2 = 0 + -8.5
-7.5m + m2 = 0 + -8.5

Combine like terms: 0 + -8.5 = -8.5
-7.5m + m2 = -8.5

The m term is -7.5m.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5m + 14.0625 + m2 = -8.5 + 14.0625

Reorder the terms:
14.0625 + -7.5m + m2 = -8.5 + 14.0625

Combine like terms: -8.5 + 14.0625 = 5.5625
14.0625 + -7.5m + m2 = 5.5625

Factor a perfect square on the left side:
(m + -3.75)(m + -3.75) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(m + -3.75) equal to 2.358495283 and -2.358495283.


Subproblem 1
m + -3.75 = 2.358495283

Simplifying
m + -3.75 = 2.358495283

Reorder the terms:
-3.75 + m = 2.358495283

Solving
-3.75 + m = 2.358495283

Solving for variable 'm'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + m = 2.358495283 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + m = 2.358495283 + 3.75
m = 2.358495283 + 3.75

Combine like terms: 2.358495283 + 3.75 = 6.108495283
m = 6.108495283

Simplifying
m = 6.108495283


Subproblem 2
m + -3.75 = -2.358495283

Simplifying
m + -3.75 = -2.358495283

Reorder the terms:
-3.75 + m = -2.358495283

Solving
-3.75 + m = -2.358495283

Solving for variable 'm'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + m = -2.358495283 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + m = -2.358495283 + 3.75
m = -2.358495283 + 3.75

Combine like terms: -2.358495283 + 3.75 = 1.391504717
m = 1.391504717

Simplifying
m = 1.391504717


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {6.108495283, 1.391504717}

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