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Simplifying m2 + -16m = 88 Reorder the terms: -16m + m2 = 88 Solving -16m + m2 = 88 Solving for variable 'm'. Reorder the terms: -88 + -16m + m2 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + -16m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + -16m + 88 + m2 = 0 + 88 Reorder the terms: -88 + 88 + -16m + m2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -16m + m2 = 0 + 88 -16m + m2 = 0 + 88 Combine like terms: 0 + 88 = 88 -16m + m2 = 88 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 = 88 + 64 Reorder the terms: 64 + -16m + m2 = 88 + 64 Combine like terms: 88 + 64 = 152 64 + -16m + m2 = 152 Factor a perfect square on the left side: (m + -8)(m + -8) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (m + -8) equal to 12.328828006 and -12.328828006.Subproblem 1
m + -8 = 12.328828006 Simplifying m + -8 = 12.328828006 Reorder the terms: -8 + m = 12.328828006 Solving -8 + m = 12.328828006 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 = 12.328828006 + 8 Combine like terms: -8 + 8 = 0 0 + m = 12.328828006 + 8 m = 12.328828006 + 8 Combine like terms: 12.328828006 + 8 = 20.328828006 m = 20.328828006 Simplifying m = 20.328828006Subproblem 2
m + -8 = -12.328828006 Simplifying m + -8 = -12.328828006 Reorder the terms: -8 + m = -12.328828006 Solving -8 + m = -12.328828006 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 = -12.328828006 + 8 Combine like terms: -8 + 8 = 0 0 + m = -12.328828006 + 8 m = -12.328828006 + 8 Combine like terms: -12.328828006 + 8 = -4.328828006 m = -4.328828006 Simplifying m = -4.328828006Solution
The solution to the problem is based on the solutions from the subproblems. m = {20.328828006, -4.328828006}
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