5m(10+12m)=17

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Solution for 5m(10+12m)=17 equation: 


Simplifying
5m(10 + 12m) = 17
(10 * 5m + 12m * 5m) = 17
(50m + 60m2) = 17

Solving
50m + 60m2 = 17

Solving for variable 'm'.

Reorder the terms:
-17 + 50m + 60m2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + 50m + 60m2 = 0

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

Divide each side by '60'.
-0.2833333333 + 0.8333333333m + m2 = 0.0

Move the constant term to the right:

Add '0.2833333333' to each side of the equation.
-0.2833333333 + 0.8333333333m + 0.2833333333 + m2 = 0.0 + 0.2833333333

Reorder the terms:
-0.2833333333 + 0.2833333333 + 0.8333333333m + m2 = 0.0 + 0.2833333333

Combine like terms: -0.2833333333 + 0.2833333333 = 0.0000000000
0.0000000000 + 0.8333333333m + m2 = 0.0 + 0.2833333333
0.8333333333m + m2 = 0.0 + 0.2833333333

Combine like terms: 0.0 + 0.2833333333 = 0.2833333333
0.8333333333m + m2 = 0.2833333333

The m term is 0.8333333333m.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333m + 0.1736111111 + m2 = 0.2833333333 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333m + m2 = 0.2833333333 + 0.1736111111

Combine like terms: 0.2833333333 + 0.1736111111 = 0.4569444444
0.1736111111 + 0.8333333333m + m2 = 0.4569444444

Factor a perfect square on the left side:
(m + 0.4166666667)(m + 0.4166666667) = 0.4569444444

Calculate the square root of the right side: 0.67597666

Break this problem into two subproblems by setting 
(m + 0.4166666667) equal to 0.67597666 and -0.67597666.


Subproblem 1
m + 0.4166666667 = 0.67597666

Simplifying
m + 0.4166666667 = 0.67597666

Reorder the terms:
0.4166666667 + m = 0.67597666

Solving
0.4166666667 + m = 0.67597666

Solving for variable 'm'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + m = 0.67597666 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + m = 0.67597666 + -0.4166666667
m = 0.67597666 + -0.4166666667

Combine like terms: 0.67597666 + -0.4166666667 = 0.2593099933
m = 0.2593099933

Simplifying
m = 0.2593099933


Subproblem 2
m + 0.4166666667 = -0.67597666

Simplifying
m + 0.4166666667 = -0.67597666

Reorder the terms:
0.4166666667 + m = -0.67597666

Solving
0.4166666667 + m = -0.67597666

Solving for variable 'm'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + m = -0.67597666 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + m = -0.67597666 + -0.4166666667
m = -0.67597666 + -0.4166666667

Combine like terms: -0.67597666 + -0.4166666667 = -1.0926433267
m = -1.0926433267

Simplifying
m = -1.0926433267


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.2593099933, -1.0926433267}

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