(9m+11)(9m+9)=79

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Solution for (9m+11)(9m+9)=79 equation:


Simplifying
(9m + 11)(9m + 9) = 79

Reorder the terms:
(11 + 9m)(9m + 9) = 79

Reorder the terms:
(11 + 9m)(9 + 9m) = 79

Multiply (11 + 9m) * (9 + 9m)
(11(9 + 9m) + 9m * (9 + 9m)) = 79
((9 * 11 + 9m * 11) + 9m * (9 + 9m)) = 79
((99 + 99m) + 9m * (9 + 9m)) = 79
(99 + 99m + (9 * 9m + 9m * 9m)) = 79
(99 + 99m + (81m + 81m2)) = 79

Combine like terms: 99m + 81m = 180m
(99 + 180m + 81m2) = 79

Solving
99 + 180m + 81m2 = 79

Solving for variable 'm'.

Reorder the terms:
99 + -79 + 180m + 81m2 = 79 + -79

Combine like terms: 99 + -79 = 20
20 + 180m + 81m2 = 79 + -79

Combine like terms: 79 + -79 = 0
20 + 180m + 81m2 = 0

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

Divide each side by '81'.
0.2469135802 + 2.222222222m + m2 = 0

Move the constant term to the right:

Add '-0.2469135802' to each side of the equation.
0.2469135802 + 2.222222222m + -0.2469135802 + m2 = 0 + -0.2469135802

Reorder the terms:
0.2469135802 + -0.2469135802 + 2.222222222m + m2 = 0 + -0.2469135802

Combine like terms: 0.2469135802 + -0.2469135802 = 0.0000000000
0.0000000000 + 2.222222222m + m2 = 0 + -0.2469135802
2.222222222m + m2 = 0 + -0.2469135802

Combine like terms: 0 + -0.2469135802 = -0.2469135802
2.222222222m + m2 = -0.2469135802

The m term is 2.222222222m.  Take half its coefficient (1.111111111).
Square it (1.234567901) and add it to both sides.

Add '1.234567901' to each side of the equation.
2.222222222m + 1.234567901 + m2 = -0.2469135802 + 1.234567901

Reorder the terms:
1.234567901 + 2.222222222m + m2 = -0.2469135802 + 1.234567901

Combine like terms: -0.2469135802 + 1.234567901 = 0.9876543208
1.234567901 + 2.222222222m + m2 = 0.9876543208

Factor a perfect square on the left side:
(m + 1.111111111)(m + 1.111111111) = 0.9876543208

Calculate the square root of the right side: 0.99380799

Break this problem into two subproblems by setting 
(m + 1.111111111) equal to 0.99380799 and -0.99380799.

Subproblem 1

m + 1.111111111 = 0.99380799 Simplifying m + 1.111111111 = 0.99380799 Reorder the terms: 1.111111111 + m = 0.99380799 Solving 1.111111111 + m = 0.99380799 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + m = 0.99380799 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + m = 0.99380799 + -1.111111111 m = 0.99380799 + -1.111111111 Combine like terms: 0.99380799 + -1.111111111 = -0.117303121 m = -0.117303121 Simplifying m = -0.117303121

Subproblem 2

m + 1.111111111 = -0.99380799 Simplifying m + 1.111111111 = -0.99380799 Reorder the terms: 1.111111111 + m = -0.99380799 Solving 1.111111111 + m = -0.99380799 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + m = -0.99380799 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + m = -0.99380799 + -1.111111111 m = -0.99380799 + -1.111111111 Combine like terms: -0.99380799 + -1.111111111 = -2.104919101 m = -2.104919101 Simplifying m = -2.104919101

Solution

The solution to the problem is based on the solutions from the subproblems. m = {-0.117303121, -2.104919101}

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