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Simplifying m2 + -16m + -95 = -12 Reorder the terms: -95 + -16m + m2 = -12 Solving -95 + -16m + m2 = -12 Solving for variable 'm'. Reorder the terms: -95 + 12 + -16m + m2 = -12 + 12 Combine like terms: -95 + 12 = -83 -83 + -16m + m2 = -12 + 12 Combine like terms: -12 + 12 = 0 -83 + -16m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '83' to each side of the equation. -83 + -16m + 83 + m2 = 0 + 83 Reorder the terms: -83 + 83 + -16m + m2 = 0 + 83 Combine like terms: -83 + 83 = 0 0 + -16m + m2 = 0 + 83 -16m + m2 = 0 + 83 Combine like terms: 0 + 83 = 83 -16m + m2 = 83 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 = 83 + 64 Reorder the terms: 64 + -16m + m2 = 83 + 64 Combine like terms: 83 + 64 = 147 64 + -16m + m2 = 147 Factor a perfect square on the left side: (m + -8)(m + -8) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (m + -8) equal to 12.124355653 and -12.124355653.Subproblem 1
m + -8 = 12.124355653 Simplifying m + -8 = 12.124355653 Reorder the terms: -8 + m = 12.124355653 Solving -8 + m = 12.124355653 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 = 12.124355653 + 8 Combine like terms: -8 + 8 = 0 0 + m = 12.124355653 + 8 m = 12.124355653 + 8 Combine like terms: 12.124355653 + 8 = 20.124355653 m = 20.124355653 Simplifying m = 20.124355653Subproblem 2
m + -8 = -12.124355653 Simplifying m + -8 = -12.124355653 Reorder the terms: -8 + m = -12.124355653 Solving -8 + m = -12.124355653 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 = -12.124355653 + 8 Combine like terms: -8 + 8 = 0 0 + m = -12.124355653 + 8 m = -12.124355653 + 8 Combine like terms: -12.124355653 + 8 = -4.124355653 m = -4.124355653 Simplifying m = -4.124355653Solution
The solution to the problem is based on the solutions from the subproblems. m = {20.124355653, -4.124355653}
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