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Simplifying m2 + 8m + 9 = 0 Reorder the terms: 9 + 8m + m2 = 0 Solving 9 + 8m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 8m + -9 + m2 = 0 + -9 Reorder the terms: 9 + -9 + 8m + m2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8m + m2 = 0 + -9 8m + m2 = 0 + -9 Combine like terms: 0 + -9 = -9 8m + m2 = -9 The m term is 8m. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8m + 16 + m2 = -9 + 16 Reorder the terms: 16 + 8m + m2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + 8m + m2 = 7 Factor a perfect square on the left side: (m + 4)(m + 4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (m + 4) equal to 2.645751311 and -2.645751311.Subproblem 1
m + 4 = 2.645751311 Simplifying m + 4 = 2.645751311 Reorder the terms: 4 + m = 2.645751311 Solving 4 + m = 2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + m = 2.645751311 + -4 m = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 m = -1.354248689 Simplifying m = -1.354248689Subproblem 2
m + 4 = -2.645751311 Simplifying m + 4 = -2.645751311 Reorder the terms: 4 + m = -2.645751311 Solving 4 + m = -2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + m = -2.645751311 + -4 m = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 m = -6.645751311 Simplifying m = -6.645751311Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.354248689, -6.645751311}
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