m^2+16m+4=0

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Solution for m^2+16m+4=0 equation:


Simplifying
m2 + 16m + 4 = 0

Reorder the terms:
4 + 16m + m2 = 0

Solving
4 + 16m + 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 + 16m + -4 + m2 = 0 + -4

Reorder the terms:
4 + -4 + 16m + m2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 16m + m2 = 0 + -4
16m + m2 = 0 + -4

Combine like terms: 0 + -4 = -4
16m + m2 = -4

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 = -4 + 64

Reorder the terms:
64 + 16m + m2 = -4 + 64

Combine like terms: -4 + 64 = 60
64 + 16m + m2 = 60

Factor a perfect square on the left side:
(m + 8)(m + 8) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(m + 8) equal to 7.745966692 and -7.745966692.

Subproblem 1

m + 8 = 7.745966692 Simplifying m + 8 = 7.745966692 Reorder the terms: 8 + m = 7.745966692 Solving 8 + m = 7.745966692 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 = 7.745966692 + -8 Combine like terms: 8 + -8 = 0 0 + m = 7.745966692 + -8 m = 7.745966692 + -8 Combine like terms: 7.745966692 + -8 = -0.254033308 m = -0.254033308 Simplifying m = -0.254033308

Subproblem 2

m + 8 = -7.745966692 Simplifying m + 8 = -7.745966692 Reorder the terms: 8 + m = -7.745966692 Solving 8 + m = -7.745966692 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 = -7.745966692 + -8 Combine like terms: 8 + -8 = 0 0 + m = -7.745966692 + -8 m = -7.745966692 + -8 Combine like terms: -7.745966692 + -8 = -15.745966692 m = -15.745966692 Simplifying m = -15.745966692

Solution

The solution to the problem is based on the solutions from the subproblems. m = {-0.254033308, -15.745966692}

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