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Simplifying m2 + 16m + -32 = 0 Reorder the terms: -32 + 16m + m2 = 0 Solving -32 + 16m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 16m + 32 + m2 = 0 + 32 Reorder the terms: -32 + 32 + 16m + m2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 16m + m2 = 0 + 32 16m + m2 = 0 + 32 Combine like terms: 0 + 32 = 32 16m + m2 = 32 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 = 32 + 64 Reorder the terms: 64 + 16m + m2 = 32 + 64 Combine like terms: 32 + 64 = 96 64 + 16m + m2 = 96 Factor a perfect square on the left side: (m + 8)(m + 8) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (m + 8) equal to 9.797958971 and -9.797958971.Subproblem 1
m + 8 = 9.797958971 Simplifying m + 8 = 9.797958971 Reorder the terms: 8 + m = 9.797958971 Solving 8 + m = 9.797958971 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 = 9.797958971 + -8 Combine like terms: 8 + -8 = 0 0 + m = 9.797958971 + -8 m = 9.797958971 + -8 Combine like terms: 9.797958971 + -8 = 1.797958971 m = 1.797958971 Simplifying m = 1.797958971Subproblem 2
m + 8 = -9.797958971 Simplifying m + 8 = -9.797958971 Reorder the terms: 8 + m = -9.797958971 Solving 8 + m = -9.797958971 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 = -9.797958971 + -8 Combine like terms: 8 + -8 = 0 0 + m = -9.797958971 + -8 m = -9.797958971 + -8 Combine like terms: -9.797958971 + -8 = -17.797958971 m = -17.797958971 Simplifying m = -17.797958971Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.797958971, -17.797958971}
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