(7m^2-9m-8)+(5m^2+10m+4)=

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Solution for (7m^2-9m-8)+(5m^2+10m+4)= equation:


Simplifying
(7m2 + -9m + -8) + (5m2 + 10m + 4) = 0

Reorder the terms:
(-8 + -9m + 7m2) + (5m2 + 10m + 4) = 0

Remove parenthesis around (-8 + -9m + 7m2)
-8 + -9m + 7m2 + (5m2 + 10m + 4) = 0

Reorder the terms:
-8 + -9m + 7m2 + (4 + 10m + 5m2) = 0

Remove parenthesis around (4 + 10m + 5m2)
-8 + -9m + 7m2 + 4 + 10m + 5m2 = 0

Reorder the terms:
-8 + 4 + -9m + 10m + 7m2 + 5m2 = 0

Combine like terms: -8 + 4 = -4
-4 + -9m + 10m + 7m2 + 5m2 = 0

Combine like terms: -9m + 10m = 1m
-4 + 1m + 7m2 + 5m2 = 0

Combine like terms: 7m2 + 5m2 = 12m2
-4 + 1m + 12m2 = 0

Solving
-4 + 1m + 12m2 = 0

Solving for variable 'm'.

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
-0.3333333333 + 0.08333333333m + m2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.08333333333m + 0.3333333333 + m2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.08333333333m + m2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.08333333333m + m2 = 0 + 0.3333333333
0.08333333333m + m2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.08333333333m + m2 = 0.3333333333

The m term is 0.08333333333m.  Take half its coefficient (0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
0.08333333333m + 0.001736111111 + m2 = 0.3333333333 + 0.001736111111

Reorder the terms:
0.001736111111 + 0.08333333333m + m2 = 0.3333333333 + 0.001736111111

Combine like terms: 0.3333333333 + 0.001736111111 = 0.335069444411
0.001736111111 + 0.08333333333m + m2 = 0.335069444411

Factor a perfect square on the left side:
(m + 0.04166666667)(m + 0.04166666667) = 0.335069444411

Calculate the square root of the right side: 0.578851833

Break this problem into two subproblems by setting 
(m + 0.04166666667) equal to 0.578851833 and -0.578851833.

Subproblem 1

m + 0.04166666667 = 0.578851833 Simplifying m + 0.04166666667 = 0.578851833 Reorder the terms: 0.04166666667 + m = 0.578851833 Solving 0.04166666667 + m = 0.578851833 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.04166666667' to each side of the equation. 0.04166666667 + -0.04166666667 + m = 0.578851833 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + m = 0.578851833 + -0.04166666667 m = 0.578851833 + -0.04166666667 Combine like terms: 0.578851833 + -0.04166666667 = 0.53718516633 m = 0.53718516633 Simplifying m = 0.53718516633

Subproblem 2

m + 0.04166666667 = -0.578851833 Simplifying m + 0.04166666667 = -0.578851833 Reorder the terms: 0.04166666667 + m = -0.578851833 Solving 0.04166666667 + m = -0.578851833 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.04166666667' to each side of the equation. 0.04166666667 + -0.04166666667 + m = -0.578851833 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + m = -0.578851833 + -0.04166666667 m = -0.578851833 + -0.04166666667 Combine like terms: -0.578851833 + -0.04166666667 = -0.62051849967 m = -0.62051849967 Simplifying m = -0.62051849967

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.53718516633, -0.62051849967}

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