-2m^2+60m=62

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Solution for -2m^2+60m=62 equation: 


Simplifying
-2m2 + 60m = 62

Reorder the terms:
60m + -2m2 = 62

Solving
60m + -2m2 = 62

Solving for variable 'm'.

Reorder the terms:
-62 + 60m + -2m2 = 62 + -62

Combine like terms: 62 + -62 = 0
-62 + 60m + -2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-31 + 30m + -1m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-31 + 30m + -1m2)' equal to zero and attempt to solve:

Simplifying
-31 + 30m + -1m2 = 0

Solving
-31 + 30m + -1m2 = 0

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

Divide each side by '-1'.
31 + -30m + m2 = 0

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + -30m + -31 + m2 = 0 + -31

Reorder the terms:
31 + -31 + -30m + m2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -30m + m2 = 0 + -31
-30m + m2 = 0 + -31

Combine like terms: 0 + -31 = -31
-30m + m2 = -31

The m term is -30m.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30m + 225 + m2 = -31 + 225

Reorder the terms:
225 + -30m + m2 = -31 + 225

Combine like terms: -31 + 225 = 194
225 + -30m + m2 = 194

Factor a perfect square on the left side:
(m + -15)(m + -15) = 194

Calculate the square root of the right side: 13.928388277

Break this problem into two subproblems by setting 
(m + -15) equal to 13.928388277 and -13.928388277.


Subproblem 1
m + -15 = 13.928388277

Simplifying
m + -15 = 13.928388277

Reorder the terms:
-15 + m = 13.928388277

Solving
-15 + m = 13.928388277

Solving for variable 'm'.

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

Add '15' to each side of the equation.
-15 + 15 + m = 13.928388277 + 15

Combine like terms: -15 + 15 = 0
0 + m = 13.928388277 + 15
m = 13.928388277 + 15

Combine like terms: 13.928388277 + 15 = 28.928388277
m = 28.928388277

Simplifying
m = 28.928388277


Subproblem 2
m + -15 = -13.928388277

Simplifying
m + -15 = -13.928388277

Reorder the terms:
-15 + m = -13.928388277

Solving
-15 + m = -13.928388277

Solving for variable 'm'.

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

Add '15' to each side of the equation.
-15 + 15 + m = -13.928388277 + 15

Combine like terms: -15 + 15 = 0
0 + m = -13.928388277 + 15
m = -13.928388277 + 15

Combine like terms: -13.928388277 + 15 = 1.071611723
m = 1.071611723

Simplifying
m = 1.071611723


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {28.928388277, 1.071611723}
Solution
m = {28.928388277, 1.071611723}

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