9m^2=25+30m

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Solution for 9m^2=25+30m equation:


Simplifying
9m2 = 25 + 30m

Solving
9m2 = 25 + 30m

Solving for variable 'm'.

Reorder the terms:
-25 + -30m + 9m2 = 25 + 30m + -25 + -30m

Reorder the terms:
-25 + -30m + 9m2 = 25 + -25 + 30m + -30m

Combine like terms: 25 + -25 = 0
-25 + -30m + 9m2 = 0 + 30m + -30m
-25 + -30m + 9m2 = 30m + -30m

Combine like terms: 30m + -30m = 0
-25 + -30m + 9m2 = 0

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

Divide each side by '9'.
-2.777777778 + -3.333333333m + m2 = 0

Move the constant term to the right:

Add '2.777777778' to each side of the equation.
-2.777777778 + -3.333333333m + 2.777777778 + m2 = 0 + 2.777777778

Reorder the terms:
-2.777777778 + 2.777777778 + -3.333333333m + m2 = 0 + 2.777777778

Combine like terms: -2.777777778 + 2.777777778 = 0.000000000
0.000000000 + -3.333333333m + m2 = 0 + 2.777777778
-3.333333333m + m2 = 0 + 2.777777778

Combine like terms: 0 + 2.777777778 = 2.777777778
-3.333333333m + m2 = 2.777777778

The m term is -3.333333333m.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333m + 2.777777779 + m2 = 2.777777778 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333m + m2 = 2.777777778 + 2.777777779

Combine like terms: 2.777777778 + 2.777777779 = 5.555555557
2.777777779 + -3.333333333m + m2 = 5.555555557

Factor a perfect square on the left side:
(m + -1.666666667)(m + -1.666666667) = 5.555555557

Calculate the square root of the right side: 2.357022604

Break this problem into two subproblems by setting 
(m + -1.666666667) equal to 2.357022604 and -2.357022604.


Subproblem 1
m + -1.666666667 = 2.357022604

Simplifying
m + -1.666666667 = 2.357022604

Reorder the terms:
-1.666666667 + m = 2.357022604

Solving
-1.666666667 + m = 2.357022604

Solving for variable 'm'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + m = 2.357022604 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + m = 2.357022604 + 1.666666667
m = 2.357022604 + 1.666666667

Combine like terms: 2.357022604 + 1.666666667 = 4.023689271
m = 4.023689271

Simplifying
m = 4.023689271


Subproblem 2
m + -1.666666667 = -2.357022604

Simplifying
m + -1.666666667 = -2.357022604

Reorder the terms:
-1.666666667 + m = -2.357022604

Solving
-1.666666667 + m = -2.357022604

Solving for variable 'm'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + m = -2.357022604 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + m = -2.357022604 + 1.666666667
m = -2.357022604 + 1.666666667

Combine like terms: -2.357022604 + 1.666666667 = -0.690355937
m = -0.690355937

Simplifying
m = -0.690355937


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.023689271, -0.690355937}

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