m^2+6m-64=0

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Solution for m^2+6m-64=0 equation:


Simplifying
m2 + 6m + -64 = 0

Reorder the terms:
-64 + 6m + m2 = 0

Solving
-64 + 6m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 6m + 64 + m2 = 0 + 64

Reorder the terms:
-64 + 64 + 6m + m2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 6m + m2 = 0 + 64
6m + m2 = 0 + 64

Combine like terms: 0 + 64 = 64
6m + m2 = 64

The m term is 6m.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6m + 9 + m2 = 64 + 9

Reorder the terms:
9 + 6m + m2 = 64 + 9

Combine like terms: 64 + 9 = 73
9 + 6m + m2 = 73

Factor a perfect square on the left side:
(m + 3)(m + 3) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(m + 3) equal to 8.544003745 and -8.544003745.

Subproblem 1

m + 3 = 8.544003745 Simplifying m + 3 = 8.544003745 Reorder the terms: 3 + m = 8.544003745 Solving 3 + m = 8.544003745 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = 8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + m = 8.544003745 + -3 m = 8.544003745 + -3 Combine like terms: 8.544003745 + -3 = 5.544003745 m = 5.544003745 Simplifying m = 5.544003745

Subproblem 2

m + 3 = -8.544003745 Simplifying m + 3 = -8.544003745 Reorder the terms: 3 + m = -8.544003745 Solving 3 + m = -8.544003745 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = -8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + m = -8.544003745 + -3 m = -8.544003745 + -3 Combine like terms: -8.544003745 + -3 = -11.544003745 m = -11.544003745 Simplifying m = -11.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. m = {5.544003745, -11.544003745}

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