3m^2-12m-10=17

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Solution for 3m^2-12m-10=17 equation: 


Simplifying
3m2 + -12m + -10 = 17

Reorder the terms:
-10 + -12m + 3m2 = 17

Solving
-10 + -12m + 3m2 = 17

Solving for variable 'm'.

Reorder the terms:
-10 + -17 + -12m + 3m2 = 17 + -17

Combine like terms: -10 + -17 = -27
-27 + -12m + 3m2 = 17 + -17

Combine like terms: 17 + -17 = 0
-27 + -12m + 3m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -4m + m2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-9 + -4m + m2)' equal to zero and attempt to solve:

Simplifying
-9 + -4m + m2 = 0

Solving
-9 + -4m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -4m + 9 + m2 = 0 + 9

Reorder the terms:
-9 + 9 + -4m + m2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4m + m2 = 0 + 9
-4m + m2 = 0 + 9

Combine like terms: 0 + 9 = 9
-4m + m2 = 9

The m term is -4m.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4m + 4 + m2 = 9 + 4

Reorder the terms:
4 + -4m + m2 = 9 + 4

Combine like terms: 9 + 4 = 13
4 + -4m + m2 = 13

Factor a perfect square on the left side:
(m + -2)(m + -2) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(m + -2) equal to 3.605551275 and -3.605551275.


Subproblem 1
m + -2 = 3.605551275

Simplifying
m + -2 = 3.605551275

Reorder the terms:
-2 + m = 3.605551275

Solving
-2 + m = 3.605551275

Solving for variable 'm'.

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

Add '2' to each side of the equation.
-2 + 2 + m = 3.605551275 + 2

Combine like terms: -2 + 2 = 0
0 + m = 3.605551275 + 2
m = 3.605551275 + 2

Combine like terms: 3.605551275 + 2 = 5.605551275
m = 5.605551275

Simplifying
m = 5.605551275


Subproblem 2
m + -2 = -3.605551275

Simplifying
m + -2 = -3.605551275

Reorder the terms:
-2 + m = -3.605551275

Solving
-2 + m = -3.605551275

Solving for variable 'm'.

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

Add '2' to each side of the equation.
-2 + 2 + m = -3.605551275 + 2

Combine like terms: -2 + 2 = 0
0 + m = -3.605551275 + 2
m = -3.605551275 + 2

Combine like terms: -3.605551275 + 2 = -1.605551275
m = -1.605551275

Simplifying
m = -1.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.605551275, -1.605551275}
Solution
m = {5.605551275, -1.605551275}

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