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Simplifying m(m + 6) = 9 Reorder the terms: m(6 + m) = 9 (6 * m + m * m) = 9 (6m + m2) = 9 Solving 6m + m2 = 9 Solving for variable 'm'. Reorder the terms: -9 + 6m + m2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 6m + 9 + m2 = 0 + 9 Reorder the terms: -9 + 9 + 6m + m2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 6m + m2 = 0 + 9 6m + m2 = 0 + 9 Combine like terms: 0 + 9 = 9 6m + m2 = 9 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 = 9 + 9 Reorder the terms: 9 + 6m + m2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + 6m + m2 = 18 Factor a perfect square on the left side: (m + 3)(m + 3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (m + 3) equal to 4.242640687 and -4.242640687.Subproblem 1
m + 3 = 4.242640687 Simplifying m + 3 = 4.242640687 Reorder the terms: 3 + m = 4.242640687 Solving 3 + m = 4.242640687 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 = 4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + m = 4.242640687 + -3 m = 4.242640687 + -3 Combine like terms: 4.242640687 + -3 = 1.242640687 m = 1.242640687 Simplifying m = 1.242640687Subproblem 2
m + 3 = -4.242640687 Simplifying m + 3 = -4.242640687 Reorder the terms: 3 + m = -4.242640687 Solving 3 + m = -4.242640687 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 = -4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + m = -4.242640687 + -3 m = -4.242640687 + -3 Combine like terms: -4.242640687 + -3 = -7.242640687 m = -7.242640687 Simplifying m = -7.242640687Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.242640687, -7.242640687}
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