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Simplifying m2 + 16m + -32 = -7 Reorder the terms: -32 + 16m + m2 = -7 Solving -32 + 16m + m2 = -7 Solving for variable 'm'. Reorder the terms: -32 + 7 + 16m + m2 = -7 + 7 Combine like terms: -32 + 7 = -25 -25 + 16m + m2 = -7 + 7 Combine like terms: -7 + 7 = 0 -25 + 16m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 16m + 25 + m2 = 0 + 25 Reorder the terms: -25 + 25 + 16m + m2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 16m + m2 = 0 + 25 16m + m2 = 0 + 25 Combine like terms: 0 + 25 = 25 16m + m2 = 25 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 = 25 + 64 Reorder the terms: 64 + 16m + m2 = 25 + 64 Combine like terms: 25 + 64 = 89 64 + 16m + m2 = 89 Factor a perfect square on the left side: (m + 8)(m + 8) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (m + 8) equal to 9.433981132 and -9.433981132.Subproblem 1
m + 8 = 9.433981132 Simplifying m + 8 = 9.433981132 Reorder the terms: 8 + m = 9.433981132 Solving 8 + m = 9.433981132 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 = 9.433981132 + -8 Combine like terms: 8 + -8 = 0 0 + m = 9.433981132 + -8 m = 9.433981132 + -8 Combine like terms: 9.433981132 + -8 = 1.433981132 m = 1.433981132 Simplifying m = 1.433981132Subproblem 2
m + 8 = -9.433981132 Simplifying m + 8 = -9.433981132 Reorder the terms: 8 + m = -9.433981132 Solving 8 + m = -9.433981132 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 = -9.433981132 + -8 Combine like terms: 8 + -8 = 0 0 + m = -9.433981132 + -8 m = -9.433981132 + -8 Combine like terms: -9.433981132 + -8 = -17.433981132 m = -17.433981132 Simplifying m = -17.433981132Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.433981132, -17.433981132}
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