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Simplifying 15m = 2m2 + -16 Reorder the terms: 15m = -16 + 2m2 Solving 15m = -16 + 2m2 Solving for variable 'm'. Reorder the terms: 16 + 15m + -2m2 = -16 + 2m2 + 16 + -2m2 Reorder the terms: 16 + 15m + -2m2 = -16 + 16 + 2m2 + -2m2 Combine like terms: -16 + 16 = 0 16 + 15m + -2m2 = 0 + 2m2 + -2m2 16 + 15m + -2m2 = 2m2 + -2m2 Combine like terms: 2m2 + -2m2 = 0 16 + 15m + -2m2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -8 + -7.5m + m2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -7.5m + 8 + m2 = 0 + 8 Reorder the terms: -8 + 8 + -7.5m + m2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7.5m + m2 = 0 + 8 -7.5m + m2 = 0 + 8 Combine like terms: 0 + 8 = 8 -7.5m + m2 = 8 The m term is -7.5m. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5m + 14.0625 + m2 = 8 + 14.0625 Reorder the terms: 14.0625 + -7.5m + m2 = 8 + 14.0625 Combine like terms: 8 + 14.0625 = 22.0625 14.0625 + -7.5m + m2 = 22.0625 Factor a perfect square on the left side: (m + -3.75)(m + -3.75) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (m + -3.75) equal to 4.697073557 and -4.697073557.Subproblem 1
m + -3.75 = 4.697073557 Simplifying m + -3.75 = 4.697073557 Reorder the terms: -3.75 + m = 4.697073557 Solving -3.75 + m = 4.697073557 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + m = 4.697073557 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + m = 4.697073557 + 3.75 m = 4.697073557 + 3.75 Combine like terms: 4.697073557 + 3.75 = 8.447073557 m = 8.447073557 Simplifying m = 8.447073557Subproblem 2
m + -3.75 = -4.697073557 Simplifying m + -3.75 = -4.697073557 Reorder the terms: -3.75 + m = -4.697073557 Solving -3.75 + m = -4.697073557 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + m = -4.697073557 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + m = -4.697073557 + 3.75 m = -4.697073557 + 3.75 Combine like terms: -4.697073557 + 3.75 = -0.947073557 m = -0.947073557 Simplifying m = -0.947073557Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.447073557, -0.947073557}
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