m^2-45m+4=0

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Solution for m^2-45m+4=0 equation: 


Simplifying
m2 + -45m + 4 = 0

Reorder the terms:
4 + -45m + m2 = 0

Solving
4 + -45m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -45m + -4 + m2 = 0 + -4

Reorder the terms:
4 + -4 + -45m + m2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -45m + m2 = 0 + -4
-45m + m2 = 0 + -4

Combine like terms: 0 + -4 = -4
-45m + m2 = -4

The m term is -45m.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45m + 506.25 + m2 = -4 + 506.25

Reorder the terms:
506.25 + -45m + m2 = -4 + 506.25

Combine like terms: -4 + 506.25 = 502.25
506.25 + -45m + m2 = 502.25

Factor a perfect square on the left side:
(m + -22.5)(m + -22.5) = 502.25

Calculate the square root of the right side: 22.410934831

Break this problem into two subproblems by setting 
(m + -22.5) equal to 22.410934831 and -22.410934831.


Subproblem 1
m + -22.5 = 22.410934831

Simplifying
m + -22.5 = 22.410934831

Reorder the terms:
-22.5 + m = 22.410934831

Solving
-22.5 + m = 22.410934831

Solving for variable 'm'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + m = 22.410934831 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + m = 22.410934831 + 22.5
m = 22.410934831 + 22.5

Combine like terms: 22.410934831 + 22.5 = 44.910934831
m = 44.910934831

Simplifying
m = 44.910934831


Subproblem 2
m + -22.5 = -22.410934831

Simplifying
m + -22.5 = -22.410934831

Reorder the terms:
-22.5 + m = -22.410934831

Solving
-22.5 + m = -22.410934831

Solving for variable 'm'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + m = -22.410934831 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + m = -22.410934831 + 22.5
m = -22.410934831 + 22.5

Combine like terms: -22.410934831 + 22.5 = 0.089065169
m = 0.089065169

Simplifying
m = 0.089065169


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {44.910934831, 0.089065169}

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