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Simplifying 15m2 + -1m + -32 = -2 + 5m Reorder the terms: -32 + -1m + 15m2 = -2 + 5m Solving -32 + -1m + 15m2 = -2 + 5m Solving for variable 'm'. Reorder the terms: -32 + 2 + -1m + -5m + 15m2 = -2 + 5m + 2 + -5m Combine like terms: -32 + 2 = -30 -30 + -1m + -5m + 15m2 = -2 + 5m + 2 + -5m Combine like terms: -1m + -5m = -6m -30 + -6m + 15m2 = -2 + 5m + 2 + -5m Reorder the terms: -30 + -6m + 15m2 = -2 + 2 + 5m + -5m Combine like terms: -2 + 2 = 0 -30 + -6m + 15m2 = 0 + 5m + -5m -30 + -6m + 15m2 = 5m + -5m Combine like terms: 5m + -5m = 0 -30 + -6m + 15m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + -2m + 5m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + -2m + 5m2)' equal to zero and attempt to solve: Simplifying -10 + -2m + 5m2 = 0 Solving -10 + -2m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -0.4m + m2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.4m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + -0.4m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.4m + m2 = 0 + 2 -0.4m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.4m + m2 = 2 The m term is -0.4m. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4m + 0.04 + m2 = 2 + 0.04 Reorder the terms: 0.04 + -0.4m + m2 = 2 + 0.04 Combine like terms: 2 + 0.04 = 2.04 0.04 + -0.4m + m2 = 2.04 Factor a perfect square on the left side: (m + -0.2)(m + -0.2) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (m + -0.2) equal to 1.428285686 and -1.428285686.Subproblem 1
m + -0.2 = 1.428285686 Simplifying m + -0.2 = 1.428285686 Reorder the terms: -0.2 + m = 1.428285686 Solving -0.2 + m = 1.428285686 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = 1.428285686 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = 1.428285686 + 0.2 m = 1.428285686 + 0.2 Combine like terms: 1.428285686 + 0.2 = 1.628285686 m = 1.628285686 Simplifying m = 1.628285686Subproblem 2
m + -0.2 = -1.428285686 Simplifying m + -0.2 = -1.428285686 Reorder the terms: -0.2 + m = -1.428285686 Solving -0.2 + m = -1.428285686 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = -1.428285686 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = -1.428285686 + 0.2 m = -1.428285686 + 0.2 Combine like terms: -1.428285686 + 0.2 = -1.228285686 m = -1.228285686 Simplifying m = -1.228285686Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.628285686, -1.228285686}Solution
m = {1.628285686, -1.228285686}
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