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Simplifying m2 + -16m + -38 = 10 Reorder the terms: -38 + -16m + m2 = 10 Solving -38 + -16m + m2 = 10 Solving for variable 'm'. Reorder the terms: -38 + -10 + -16m + m2 = 10 + -10 Combine like terms: -38 + -10 = -48 -48 + -16m + m2 = 10 + -10 Combine like terms: 10 + -10 = 0 -48 + -16m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -16m + 48 + m2 = 0 + 48 Reorder the terms: -48 + 48 + -16m + m2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -16m + m2 = 0 + 48 -16m + m2 = 0 + 48 Combine like terms: 0 + 48 = 48 -16m + m2 = 48 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 = 48 + 64 Reorder the terms: 64 + -16m + m2 = 48 + 64 Combine like terms: 48 + 64 = 112 64 + -16m + m2 = 112 Factor a perfect square on the left side: (m + -8)(m + -8) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (m + -8) equal to 10.583005244 and -10.583005244.Subproblem 1
m + -8 = 10.583005244 Simplifying m + -8 = 10.583005244 Reorder the terms: -8 + m = 10.583005244 Solving -8 + m = 10.583005244 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 = 10.583005244 + 8 Combine like terms: -8 + 8 = 0 0 + m = 10.583005244 + 8 m = 10.583005244 + 8 Combine like terms: 10.583005244 + 8 = 18.583005244 m = 18.583005244 Simplifying m = 18.583005244Subproblem 2
m + -8 = -10.583005244 Simplifying m + -8 = -10.583005244 Reorder the terms: -8 + m = -10.583005244 Solving -8 + m = -10.583005244 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 = -10.583005244 + 8 Combine like terms: -8 + 8 = 0 0 + m = -10.583005244 + 8 m = -10.583005244 + 8 Combine like terms: -10.583005244 + 8 = -2.583005244 m = -2.583005244 Simplifying m = -2.583005244Solution
The solution to the problem is based on the solutions from the subproblems. m = {18.583005244, -2.583005244}
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