10=5m(m-5)

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Solution for 10=5m(m-5) equation: 


Simplifying
10 = 5m(m + -5)

Reorder the terms:
10 = 5m(-5 + m)
10 = (-5 * 5m + m * 5m)
10 = (-25m + 5m2)

Solving
10 = -25m + 5m2

Solving for variable 'm'.

Reorder the terms:
10 + 25m + -5m2 = -25m + 25m + 5m2 + -5m2

Combine like terms: -25m + 25m = 0
10 + 25m + -5m2 = 0 + 5m2 + -5m2
10 + 25m + -5m2 = 5m2 + -5m2

Combine like terms: 5m2 + -5m2 = 0
10 + 25m + -5m2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + 5m + -1m2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + 5m + -1m2)' equal to zero and attempt to solve:

Simplifying
2 + 5m + -1m2 = 0

Solving
2 + 5m + -1m2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -5m + m2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -5m + 2 + m2 = 0 + 2

Reorder the terms:
-2 + 2 + -5m + m2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5m + m2 = 0 + 2
-5m + m2 = 0 + 2

Combine like terms: 0 + 2 = 2
-5m + m2 = 2

The m term is -5m.  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.
-5m + 6.25 + m2 = 2 + 6.25

Reorder the terms:
6.25 + -5m + m2 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + -5m + m2 = 8.25

Factor a perfect square on the left side:
(m + -2.5)(m + -2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(m + -2.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
m + -2.5 = 2.872281323

Simplifying
m + -2.5 = 2.872281323

Reorder the terms:
-2.5 + m = 2.872281323

Solving
-2.5 + m = 2.872281323

Solving for variable 'm'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + m = 2.872281323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + m = 2.872281323 + 2.5
m = 2.872281323 + 2.5

Combine like terms: 2.872281323 + 2.5 = 5.372281323
m = 5.372281323

Simplifying
m = 5.372281323


Subproblem 2
m + -2.5 = -2.872281323

Simplifying
m + -2.5 = -2.872281323

Reorder the terms:
-2.5 + m = -2.872281323

Solving
-2.5 + m = -2.872281323

Solving for variable 'm'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + m = -2.872281323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + m = -2.872281323 + 2.5
m = -2.872281323 + 2.5

Combine like terms: -2.872281323 + 2.5 = -0.372281323
m = -0.372281323

Simplifying
m = -0.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.372281323, -0.372281323}
Solution
m = {5.372281323, -0.372281323}

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