m^2+23m+24=1

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Solution for m^2+23m+24=1 equation: 


Simplifying
m2 + 23m + 24 = 1

Reorder the terms:
24 + 23m + m2 = 1

Solving
24 + 23m + m2 = 1

Solving for variable 'm'.

Reorder the terms:
24 + -1 + 23m + m2 = 1 + -1

Combine like terms: 24 + -1 = 23
23 + 23m + m2 = 1 + -1

Combine like terms: 1 + -1 = 0
23 + 23m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + 23m + -23 + m2 = 0 + -23

Reorder the terms:
23 + -23 + 23m + m2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 23m + m2 = 0 + -23
23m + m2 = 0 + -23

Combine like terms: 0 + -23 = -23
23m + m2 = -23

The m term is 23m.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23m + 132.25 + m2 = -23 + 132.25

Reorder the terms:
132.25 + 23m + m2 = -23 + 132.25

Combine like terms: -23 + 132.25 = 109.25
132.25 + 23m + m2 = 109.25

Factor a perfect square on the left side:
(m + 11.5)(m + 11.5) = 109.25

Calculate the square root of the right side: 10.45227248

Break this problem into two subproblems by setting 
(m + 11.5) equal to 10.45227248 and -10.45227248.


Subproblem 1
m + 11.5 = 10.45227248

Simplifying
m + 11.5 = 10.45227248

Reorder the terms:
11.5 + m = 10.45227248

Solving
11.5 + m = 10.45227248

Solving for variable 'm'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + m = 10.45227248 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + m = 10.45227248 + -11.5
m = 10.45227248 + -11.5

Combine like terms: 10.45227248 + -11.5 = -1.04772752
m = -1.04772752

Simplifying
m = -1.04772752


Subproblem 2
m + 11.5 = -10.45227248

Simplifying
m + 11.5 = -10.45227248

Reorder the terms:
11.5 + m = -10.45227248

Solving
11.5 + m = -10.45227248

Solving for variable 'm'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + m = -10.45227248 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + m = -10.45227248 + -11.5
m = -10.45227248 + -11.5

Combine like terms: -10.45227248 + -11.5 = -21.95227248
m = -21.95227248

Simplifying
m = -21.95227248


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-1.04772752, -21.95227248}

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