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Simplifying m2 + 16m + 64 = 5 Reorder the terms: 64 + 16m + m2 = 5 Solving 64 + 16m + m2 = 5 Solving for variable 'm'. Reorder the terms: 64 + -5 + 16m + m2 = 5 + -5 Combine like terms: 64 + -5 = 59 59 + 16m + m2 = 5 + -5 Combine like terms: 5 + -5 = 0 59 + 16m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 16m + -59 + m2 = 0 + -59 Reorder the terms: 59 + -59 + 16m + m2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 16m + m2 = 0 + -59 16m + m2 = 0 + -59 Combine like terms: 0 + -59 = -59 16m + m2 = -59 The m term is 16m. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16m + 64 + m2 = -59 + 64 Reorder the terms: 64 + 16m + m2 = -59 + 64 Combine like terms: -59 + 64 = 5 64 + 16m + m2 = 5 Factor a perfect square on the left side: (m + 8)(m + 8) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (m + 8) equal to 2.236067978 and -2.236067978.Subproblem 1
m + 8 = 2.236067978 Simplifying m + 8 = 2.236067978 Reorder the terms: 8 + m = 2.236067978 Solving 8 + m = 2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + m = 2.236067978 + -8 Combine like terms: 8 + -8 = 0 0 + m = 2.236067978 + -8 m = 2.236067978 + -8 Combine like terms: 2.236067978 + -8 = -5.763932022 m = -5.763932022 Simplifying m = -5.763932022Subproblem 2
m + 8 = -2.236067978 Simplifying m + 8 = -2.236067978 Reorder the terms: 8 + m = -2.236067978 Solving 8 + m = -2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + m = -2.236067978 + -8 Combine like terms: 8 + -8 = 0 0 + m = -2.236067978 + -8 m = -2.236067978 + -8 Combine like terms: -2.236067978 + -8 = -10.236067978 m = -10.236067978 Simplifying m = -10.236067978Solution
The solution to the problem is based on the solutions from the subproblems. m = {-5.763932022, -10.236067978}
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