m^2=41-4m

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Solution for m^2=41-4m equation:


Simplifying
m2 = 41 + -4m

Solving
m2 = 41 + -4m

Solving for variable 'm'.

Reorder the terms:
-41 + 4m + m2 = 41 + -4m + -41 + 4m

Reorder the terms:
-41 + 4m + m2 = 41 + -41 + -4m + 4m

Combine like terms: 41 + -41 = 0
-41 + 4m + m2 = 0 + -4m + 4m
-41 + 4m + m2 = -4m + 4m

Combine like terms: -4m + 4m = 0
-41 + 4m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 4m + 41 + m2 = 0 + 41

Reorder the terms:
-41 + 41 + 4m + m2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 4m + m2 = 0 + 41
4m + m2 = 0 + 41

Combine like terms: 0 + 41 = 41
4m + m2 = 41

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 = 41 + 4

Reorder the terms:
4 + 4m + m2 = 41 + 4

Combine like terms: 41 + 4 = 45
4 + 4m + m2 = 45

Factor a perfect square on the left side:
(m + 2)(m + 2) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(m + 2) equal to 6.708203933 and -6.708203933.

Subproblem 1

m + 2 = 6.708203933 Simplifying m + 2 = 6.708203933 Reorder the terms: 2 + m = 6.708203933 Solving 2 + m = 6.708203933 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 = 6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + m = 6.708203933 + -2 m = 6.708203933 + -2 Combine like terms: 6.708203933 + -2 = 4.708203933 m = 4.708203933 Simplifying m = 4.708203933

Subproblem 2

m + 2 = -6.708203933 Simplifying m + 2 = -6.708203933 Reorder the terms: 2 + m = -6.708203933 Solving 2 + m = -6.708203933 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 = -6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + m = -6.708203933 + -2 m = -6.708203933 + -2 Combine like terms: -6.708203933 + -2 = -8.708203933 m = -8.708203933 Simplifying m = -8.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. m = {4.708203933, -8.708203933}

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