m^2+16m=59

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


Simplifying
m2 + 16m = 59

Reorder the terms:
16m + m2 = 59

Solving
16m + m2 = 59

Solving for variable 'm'.

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

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

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 = 123
64 + 16m + m2 = 123

Factor a perfect square on the left side:
(m + 8)(m + 8) = 123

Calculate the square root of the right side: 11.090536506

Break this problem into two subproblems by setting 
(m + 8) equal to 11.090536506 and -11.090536506.

Subproblem 1

m + 8 = 11.090536506 Simplifying m + 8 = 11.090536506 Reorder the terms: 8 + m = 11.090536506 Solving 8 + m = 11.090536506 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 = 11.090536506 + -8 Combine like terms: 8 + -8 = 0 0 + m = 11.090536506 + -8 m = 11.090536506 + -8 Combine like terms: 11.090536506 + -8 = 3.090536506 m = 3.090536506 Simplifying m = 3.090536506

Subproblem 2

m + 8 = -11.090536506 Simplifying m + 8 = -11.090536506 Reorder the terms: 8 + m = -11.090536506 Solving 8 + m = -11.090536506 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 = -11.090536506 + -8 Combine like terms: 8 + -8 = 0 0 + m = -11.090536506 + -8 m = -11.090536506 + -8 Combine like terms: -11.090536506 + -8 = -19.090536506 m = -19.090536506 Simplifying m = -19.090536506

Solution

The solution to the problem is based on the solutions from the subproblems. m = {3.090536506, -19.090536506}

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