7(7+5m)+m(m+6)4=

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Solution for 7(7+5m)+m(m+6)4= equation:


Simplifying
7(7 + 5m) + m(m + 6) * 4 = 0
(7 * 7 + 5m * 7) + m(m + 6) * 4 = 0
(49 + 35m) + m(m + 6) * 4 = 0

Reorder the terms:
49 + 35m + m(6 + m) * 4 = 0

Reorder the terms for easier multiplication:
49 + 35m + 4m(6 + m) = 0
49 + 35m + (6 * 4m + m * 4m) = 0
49 + 35m + (24m + 4m2) = 0

Combine like terms: 35m + 24m = 59m
49 + 59m + 4m2 = 0

Solving
49 + 59m + 4m2 = 0

Solving for variable 'm'.

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

Divide each side by '4'.
12.25 + 14.75m + m2 = 0

Move the constant term to the right:

Add '-12.25' to each side of the equation.
12.25 + 14.75m + -12.25 + m2 = 0 + -12.25

Reorder the terms:
12.25 + -12.25 + 14.75m + m2 = 0 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
0.00 + 14.75m + m2 = 0 + -12.25
14.75m + m2 = 0 + -12.25

Combine like terms: 0 + -12.25 = -12.25
14.75m + m2 = -12.25

The m term is 14.75m.  Take half its coefficient (7.375).
Square it (54.390625) and add it to both sides.

Add '54.390625' to each side of the equation.
14.75m + 54.390625 + m2 = -12.25 + 54.390625

Reorder the terms:
54.390625 + 14.75m + m2 = -12.25 + 54.390625

Combine like terms: -12.25 + 54.390625 = 42.140625
54.390625 + 14.75m + m2 = 42.140625

Factor a perfect square on the left side:
(m + 7.375)(m + 7.375) = 42.140625

Calculate the square root of the right side: 6.491581086

Break this problem into two subproblems by setting 
(m + 7.375) equal to 6.491581086 and -6.491581086.

Subproblem 1

m + 7.375 = 6.491581086 Simplifying m + 7.375 = 6.491581086 Reorder the terms: 7.375 + m = 6.491581086 Solving 7.375 + m = 6.491581086 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7.375' to each side of the equation. 7.375 + -7.375 + m = 6.491581086 + -7.375 Combine like terms: 7.375 + -7.375 = 0.000 0.000 + m = 6.491581086 + -7.375 m = 6.491581086 + -7.375 Combine like terms: 6.491581086 + -7.375 = -0.883418914 m = -0.883418914 Simplifying m = -0.883418914

Subproblem 2

m + 7.375 = -6.491581086 Simplifying m + 7.375 = -6.491581086 Reorder the terms: 7.375 + m = -6.491581086 Solving 7.375 + m = -6.491581086 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7.375' to each side of the equation. 7.375 + -7.375 + m = -6.491581086 + -7.375 Combine like terms: 7.375 + -7.375 = 0.000 0.000 + m = -6.491581086 + -7.375 m = -6.491581086 + -7.375 Combine like terms: -6.491581086 + -7.375 = -13.866581086 m = -13.866581086 Simplifying m = -13.866581086

Solution

The solution to the problem is based on the solutions from the subproblems. m = {-0.883418914, -13.866581086}

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