9m^2-30m+25=30

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


Simplifying
9m2 + -30m + 25 = 30

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

Solving
25 + -30m + 9m2 = 30

Solving for variable 'm'.

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

Combine like terms: 25 + -30 = -5
-5 + -30m + 9m2 = 30 + -30

Combine like terms: 30 + -30 = 0
-5 + -30m + 9m2 = 0

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

Divide each side by '9'.
-0.5555555556 + -3.333333333m + m2 = 0

Move the constant term to the right:

Add '0.5555555556' to each side of the equation.
-0.5555555556 + -3.333333333m + 0.5555555556 + m2 = 0 + 0.5555555556

Reorder the terms:
-0.5555555556 + 0.5555555556 + -3.333333333m + m2 = 0 + 0.5555555556

Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000
0.0000000000 + -3.333333333m + m2 = 0 + 0.5555555556
-3.333333333m + m2 = 0 + 0.5555555556

Combine like terms: 0 + 0.5555555556 = 0.5555555556
-3.333333333m + m2 = 0.5555555556

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 = 0.5555555556 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333m + m2 = 0.5555555556 + 2.777777779

Combine like terms: 0.5555555556 + 2.777777779 = 3.3333333346
2.777777779 + -3.333333333m + m2 = 3.3333333346

Factor a perfect square on the left side:
(m + -1.666666667)(m + -1.666666667) = 3.3333333346

Calculate the square root of the right side: 1.825741859

Break this problem into two subproblems by setting 
(m + -1.666666667) equal to 1.825741859 and -1.825741859.

Subproblem 1

m + -1.666666667 = 1.825741859 Simplifying m + -1.666666667 = 1.825741859 Reorder the terms: -1.666666667 + m = 1.825741859 Solving -1.666666667 + m = 1.825741859 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 = 1.825741859 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + m = 1.825741859 + 1.666666667 m = 1.825741859 + 1.666666667 Combine like terms: 1.825741859 + 1.666666667 = 3.492408526 m = 3.492408526 Simplifying m = 3.492408526

Subproblem 2

m + -1.666666667 = -1.825741859 Simplifying m + -1.666666667 = -1.825741859 Reorder the terms: -1.666666667 + m = -1.825741859 Solving -1.666666667 + m = -1.825741859 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 = -1.825741859 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + m = -1.825741859 + 1.666666667 m = -1.825741859 + 1.666666667 Combine like terms: -1.825741859 + 1.666666667 = -0.159075192 m = -0.159075192 Simplifying m = -0.159075192

Solution

The solution to the problem is based on the solutions from the subproblems. m = {3.492408526, -0.159075192}

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