(25-m)(10-m)=10

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Solution for (25-m)(10-m)=10 equation: 


Simplifying
(25 + -1m)(10 + -1m) = 10

Multiply (25 + -1m) * (10 + -1m)
(25(10 + -1m) + -1m * (10 + -1m)) = 10
((10 * 25 + -1m * 25) + -1m * (10 + -1m)) = 10
((250 + -25m) + -1m * (10 + -1m)) = 10
(250 + -25m + (10 * -1m + -1m * -1m)) = 10
(250 + -25m + (-10m + 1m2)) = 10

Combine like terms: -25m + -10m = -35m
(250 + -35m + 1m2) = 10

Solving
250 + -35m + 1m2 = 10

Solving for variable 'm'.

Reorder the terms:
250 + -10 + -35m + 1m2 = 10 + -10

Combine like terms: 250 + -10 = 240
240 + -35m + 1m2 = 10 + -10

Combine like terms: 10 + -10 = 0
240 + -35m + 1m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-240' to each side of the equation.
240 + -35m + -240 + m2 = 0 + -240

Reorder the terms:
240 + -240 + -35m + m2 = 0 + -240

Combine like terms: 240 + -240 = 0
0 + -35m + m2 = 0 + -240
-35m + m2 = 0 + -240

Combine like terms: 0 + -240 = -240
-35m + m2 = -240

The m term is -35m.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35m + 306.25 + m2 = -240 + 306.25

Reorder the terms:
306.25 + -35m + m2 = -240 + 306.25

Combine like terms: -240 + 306.25 = 66.25
306.25 + -35m + m2 = 66.25

Factor a perfect square on the left side:
(m + -17.5)(m + -17.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(m + -17.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
m + -17.5 = 8.139410298

Simplifying
m + -17.5 = 8.139410298

Reorder the terms:
-17.5 + m = 8.139410298

Solving
-17.5 + m = 8.139410298

Solving for variable 'm'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + m = 8.139410298 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + m = 8.139410298 + 17.5
m = 8.139410298 + 17.5

Combine like terms: 8.139410298 + 17.5 = 25.639410298
m = 25.639410298

Simplifying
m = 25.639410298


Subproblem 2
m + -17.5 = -8.139410298

Simplifying
m + -17.5 = -8.139410298

Reorder the terms:
-17.5 + m = -8.139410298

Solving
-17.5 + m = -8.139410298

Solving for variable 'm'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + m = -8.139410298 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + m = -8.139410298 + 17.5
m = -8.139410298 + 17.5

Combine like terms: -8.139410298 + 17.5 = 9.360589702
m = 9.360589702

Simplifying
m = 9.360589702


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {25.639410298, 9.360589702}

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