m^2+16m+59=0

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Solution for m^2+16m+59=0 equation:


Simplifying
m2 + 16m + 59 = 0

Reorder the terms:
59 + 16m + m2 = 0

Solving
59 + 16m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-59' to each side of the equation.
59 + 16m + -59 + m2 = 0 + -59

Reorder the terms:
59 + -59 + 16m + m2 = 0 + -59

Combine like terms: 59 + -59 = 0
0 + 16m + m2 = 0 + -59
16m + m2 = 0 + -59

Combine like terms: 0 + -59 = -59
16m + m2 = -59

The m term is 16m.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16m + 64 + m2 = -59 + 64

Reorder the terms:
64 + 16m + m2 = -59 + 64

Combine like terms: -59 + 64 = 5
64 + 16m + m2 = 5

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

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(m + 8) equal to 2.236067978 and -2.236067978.

Subproblem 1

m + 8 = 2.236067978 Simplifying m + 8 = 2.236067978 Reorder the terms: 8 + m = 2.236067978 Solving 8 + m = 2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + m = 2.236067978 + -8 Combine like terms: 8 + -8 = 0 0 + m = 2.236067978 + -8 m = 2.236067978 + -8 Combine like terms: 2.236067978 + -8 = -5.763932022 m = -5.763932022 Simplifying m = -5.763932022

Subproblem 2

m + 8 = -2.236067978 Simplifying m + 8 = -2.236067978 Reorder the terms: 8 + m = -2.236067978 Solving 8 + m = -2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + m = -2.236067978 + -8 Combine like terms: 8 + -8 = 0 0 + m = -2.236067978 + -8 m = -2.236067978 + -8 Combine like terms: -2.236067978 + -8 = -10.236067978 m = -10.236067978 Simplifying m = -10.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. m = {-5.763932022, -10.236067978}

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