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Simplifying m2 + -6m + -53 = 5 Reorder the terms: -53 + -6m + m2 = 5 Solving -53 + -6m + m2 = 5 Solving for variable 'm'. Reorder the terms: -53 + -5 + -6m + m2 = 5 + -5 Combine like terms: -53 + -5 = -58 -58 + -6m + m2 = 5 + -5 Combine like terms: 5 + -5 = 0 -58 + -6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + -6m + 58 + m2 = 0 + 58 Reorder the terms: -58 + 58 + -6m + m2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + -6m + m2 = 0 + 58 -6m + m2 = 0 + 58 Combine like terms: 0 + 58 = 58 -6m + m2 = 58 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 = 58 + 9 Reorder the terms: 9 + -6m + m2 = 58 + 9 Combine like terms: 58 + 9 = 67 9 + -6m + m2 = 67 Factor a perfect square on the left side: (m + -3)(m + -3) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (m + -3) equal to 8.185352772 and -8.185352772.Subproblem 1
m + -3 = 8.185352772 Simplifying m + -3 = 8.185352772 Reorder the terms: -3 + m = 8.185352772 Solving -3 + m = 8.185352772 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 = 8.185352772 + 3 Combine like terms: -3 + 3 = 0 0 + m = 8.185352772 + 3 m = 8.185352772 + 3 Combine like terms: 8.185352772 + 3 = 11.185352772 m = 11.185352772 Simplifying m = 11.185352772Subproblem 2
m + -3 = -8.185352772 Simplifying m + -3 = -8.185352772 Reorder the terms: -3 + m = -8.185352772 Solving -3 + m = -8.185352772 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 = -8.185352772 + 3 Combine like terms: -3 + 3 = 0 0 + m = -8.185352772 + 3 m = -8.185352772 + 3 Combine like terms: -8.185352772 + 3 = -5.185352772 m = -5.185352772 Simplifying m = -5.185352772Solution
The solution to the problem is based on the solutions from the subproblems. m = {11.185352772, -5.185352772}
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