2m^2-20m+51=17

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Solution for 2m^2-20m+51=17 equation: 


Simplifying
2m2 + -20m + 51 = 17

Reorder the terms:
51 + -20m + 2m2 = 17

Solving
51 + -20m + 2m2 = 17

Solving for variable 'm'.

Reorder the terms:
51 + -17 + -20m + 2m2 = 17 + -17

Combine like terms: 51 + -17 = 34
34 + -20m + 2m2 = 17 + -17

Combine like terms: 17 + -17 = 0
34 + -20m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -10m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + -10m + m2)' equal to zero and attempt to solve:

Simplifying
17 + -10m + m2 = 0

Solving
17 + -10m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -10m + -17 + m2 = 0 + -17

Reorder the terms:
17 + -17 + -10m + m2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -10m + m2 = 0 + -17
-10m + m2 = 0 + -17

Combine like terms: 0 + -17 = -17
-10m + m2 = -17

The m term is -10m.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10m + 25 + m2 = -17 + 25

Reorder the terms:
25 + -10m + m2 = -17 + 25

Combine like terms: -17 + 25 = 8
25 + -10m + m2 = 8

Factor a perfect square on the left side:
(m + -5)(m + -5) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(m + -5) equal to 2.828427125 and -2.828427125.


Subproblem 1
m + -5 = 2.828427125

Simplifying
m + -5 = 2.828427125

Reorder the terms:
-5 + m = 2.828427125

Solving
-5 + m = 2.828427125

Solving for variable 'm'.

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

Add '5' to each side of the equation.
-5 + 5 + m = 2.828427125 + 5

Combine like terms: -5 + 5 = 0
0 + m = 2.828427125 + 5
m = 2.828427125 + 5

Combine like terms: 2.828427125 + 5 = 7.828427125
m = 7.828427125

Simplifying
m = 7.828427125


Subproblem 2
m + -5 = -2.828427125

Simplifying
m + -5 = -2.828427125

Reorder the terms:
-5 + m = -2.828427125

Solving
-5 + m = -2.828427125

Solving for variable 'm'.

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

Add '5' to each side of the equation.
-5 + 5 + m = -2.828427125 + 5

Combine like terms: -5 + 5 = 0
0 + m = -2.828427125 + 5
m = -2.828427125 + 5

Combine like terms: -2.828427125 + 5 = 2.171572875
m = 2.171572875

Simplifying
m = 2.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {7.828427125, 2.171572875}
Solution
m = {7.828427125, 2.171572875}

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