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 = 68
64 + 16m + m2 = 68

Factor a perfect square on the left side:
(m + 8)(m + 8) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(m + 8) equal to 8.246211251 and -8.246211251.

Subproblem 1

m + 8 = 8.246211251 Simplifying m + 8 = 8.246211251 Reorder the terms: 8 + m = 8.246211251 Solving 8 + m = 8.246211251 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 = 8.246211251 + -8 Combine like terms: 8 + -8 = 0 0 + m = 8.246211251 + -8 m = 8.246211251 + -8 Combine like terms: 8.246211251 + -8 = 0.246211251 m = 0.246211251 Simplifying m = 0.246211251

Subproblem 2

m + 8 = -8.246211251 Simplifying m + 8 = -8.246211251 Reorder the terms: 8 + m = -8.246211251 Solving 8 + m = -8.246211251 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 = -8.246211251 + -8 Combine like terms: 8 + -8 = 0 0 + m = -8.246211251 + -8 m = -8.246211251 + -8 Combine like terms: -8.246211251 + -8 = -16.246211251 m = -16.246211251 Simplifying m = -16.246211251

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.246211251, -16.246211251}

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