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Simplifying m * m + 6m = -2 Multiply m * m m2 + 6m = -2 Reorder the terms: 6m + m2 = -2 Solving 6m + m2 = -2 Solving for variable 'm'. Reorder the terms: 2 + 6m + m2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 6m + -2 + m2 = 0 + -2 Reorder the terms: 2 + -2 + 6m + m2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6m + m2 = 0 + -2 6m + m2 = 0 + -2 Combine like terms: 0 + -2 = -2 6m + m2 = -2 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 = -2 + 9 Reorder the terms: 9 + 6m + m2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + 6m + m2 = 7 Factor a perfect square on the left side: (m + 3)(m + 3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (m + 3) equal to 2.645751311 and -2.645751311.Subproblem 1
m + 3 = 2.645751311 Simplifying m + 3 = 2.645751311 Reorder the terms: 3 + m = 2.645751311 Solving 3 + m = 2.645751311 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 = 2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + m = 2.645751311 + -3 m = 2.645751311 + -3 Combine like terms: 2.645751311 + -3 = -0.354248689 m = -0.354248689 Simplifying m = -0.354248689Subproblem 2
m + 3 = -2.645751311 Simplifying m + 3 = -2.645751311 Reorder the terms: 3 + m = -2.645751311 Solving 3 + m = -2.645751311 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 = -2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + m = -2.645751311 + -3 m = -2.645751311 + -3 Combine like terms: -2.645751311 + -3 = -5.645751311 m = -5.645751311 Simplifying m = -5.645751311Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.354248689, -5.645751311}
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