3m^2+228m-1000=2900

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Solution for 3m^2+228m-1000=2900 equation: 


Simplifying
3m2 + 228m + -1000 = 2900

Reorder the terms:
-1000 + 228m + 3m2 = 2900

Solving
-1000 + 228m + 3m2 = 2900

Solving for variable 'm'.

Reorder the terms:
-1000 + -2900 + 228m + 3m2 = 2900 + -2900

Combine like terms: -1000 + -2900 = -3900
-3900 + 228m + 3m2 = 2900 + -2900

Combine like terms: 2900 + -2900 = 0
-3900 + 228m + 3m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1300 + 76m + m2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1300 + 76m + m2)' equal to zero and attempt to solve:

Simplifying
-1300 + 76m + m2 = 0

Solving
-1300 + 76m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1300' to each side of the equation.
-1300 + 76m + 1300 + m2 = 0 + 1300

Reorder the terms:
-1300 + 1300 + 76m + m2 = 0 + 1300

Combine like terms: -1300 + 1300 = 0
0 + 76m + m2 = 0 + 1300
76m + m2 = 0 + 1300

Combine like terms: 0 + 1300 = 1300
76m + m2 = 1300

The m term is 76m.  Take half its coefficient (38).
Square it (1444) and add it to both sides.

Add '1444' to each side of the equation.
76m + 1444 + m2 = 1300 + 1444

Reorder the terms:
1444 + 76m + m2 = 1300 + 1444

Combine like terms: 1300 + 1444 = 2744
1444 + 76m + m2 = 2744

Factor a perfect square on the left side:
(m + 38)(m + 38) = 2744

Calculate the square root of the right side: 52.383203415

Break this problem into two subproblems by setting 
(m + 38) equal to 52.383203415 and -52.383203415.


Subproblem 1
m + 38 = 52.383203415

Simplifying
m + 38 = 52.383203415

Reorder the terms:
38 + m = 52.383203415

Solving
38 + m = 52.383203415

Solving for variable 'm'.

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

Add '-38' to each side of the equation.
38 + -38 + m = 52.383203415 + -38

Combine like terms: 38 + -38 = 0
0 + m = 52.383203415 + -38
m = 52.383203415 + -38

Combine like terms: 52.383203415 + -38 = 14.383203415
m = 14.383203415

Simplifying
m = 14.383203415


Subproblem 2
m + 38 = -52.383203415

Simplifying
m + 38 = -52.383203415

Reorder the terms:
38 + m = -52.383203415

Solving
38 + m = -52.383203415

Solving for variable 'm'.

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

Add '-38' to each side of the equation.
38 + -38 + m = -52.383203415 + -38

Combine like terms: 38 + -38 = 0
0 + m = -52.383203415 + -38
m = -52.383203415 + -38

Combine like terms: -52.383203415 + -38 = -90.383203415
m = -90.383203415

Simplifying
m = -90.383203415


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {14.383203415, -90.383203415}
Solution
m = {14.383203415, -90.383203415}

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