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Simplifying -1m2 + 16m = -8 Reorder the terms: 16m + -1m2 = -8 Solving 16m + -1m2 = -8 Solving for variable 'm'. Reorder the terms: 8 + 16m + -1m2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 16m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -16m + m2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -16m + 8 + m2 = 0 + 8 Reorder the terms: -8 + 8 + -16m + m2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -16m + m2 = 0 + 8 -16m + m2 = 0 + 8 Combine like terms: 0 + 8 = 8 -16m + m2 = 8 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 = 8 + 64 Reorder the terms: 64 + -16m + m2 = 8 + 64 Combine like terms: 8 + 64 = 72 64 + -16m + m2 = 72 Factor a perfect square on the left side: (m + -8)(m + -8) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (m + -8) equal to 8.485281374 and -8.485281374.Subproblem 1
m + -8 = 8.485281374 Simplifying m + -8 = 8.485281374 Reorder the terms: -8 + m = 8.485281374 Solving -8 + m = 8.485281374 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 = 8.485281374 + 8 Combine like terms: -8 + 8 = 0 0 + m = 8.485281374 + 8 m = 8.485281374 + 8 Combine like terms: 8.485281374 + 8 = 16.485281374 m = 16.485281374 Simplifying m = 16.485281374Subproblem 2
m + -8 = -8.485281374 Simplifying m + -8 = -8.485281374 Reorder the terms: -8 + m = -8.485281374 Solving -8 + m = -8.485281374 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 = -8.485281374 + 8 Combine like terms: -8 + 8 = 0 0 + m = -8.485281374 + 8 m = -8.485281374 + 8 Combine like terms: -8.485281374 + 8 = -0.485281374 m = -0.485281374 Simplifying m = -0.485281374Solution
The solution to the problem is based on the solutions from the subproblems. m = {16.485281374, -0.485281374}
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