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Simplifying m2 + -8m + -16 = 0 Reorder the terms: -16 + -8m + m2 = 0 Solving -16 + -8m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -8m + 16 + m2 = 0 + 16 Reorder the terms: -16 + 16 + -8m + m2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -8m + m2 = 0 + 16 -8m + m2 = 0 + 16 Combine like terms: 0 + 16 = 16 -8m + m2 = 16 The m term is -8m. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8m + 16 + m2 = 16 + 16 Reorder the terms: 16 + -8m + m2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + -8m + m2 = 32 Factor a perfect square on the left side: (m + -4)(m + -4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (m + -4) equal to 5.656854249 and -5.656854249.Subproblem 1
m + -4 = 5.656854249 Simplifying m + -4 = 5.656854249 Reorder the terms: -4 + m = 5.656854249 Solving -4 + m = 5.656854249 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + m = 5.656854249 + 4 m = 5.656854249 + 4 Combine like terms: 5.656854249 + 4 = 9.656854249 m = 9.656854249 Simplifying m = 9.656854249Subproblem 2
m + -4 = -5.656854249 Simplifying m + -4 = -5.656854249 Reorder the terms: -4 + m = -5.656854249 Solving -4 + m = -5.656854249 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + m = -5.656854249 + 4 m = -5.656854249 + 4 Combine like terms: -5.656854249 + 4 = -1.656854249 m = -1.656854249 Simplifying m = -1.656854249Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.656854249, -1.656854249}
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