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Simplifying (10m + 300) + -1(0.6m2 + -5m + 24) = 0 Reorder the terms: (300 + 10m) + -1(0.6m2 + -5m + 24) = 0 Remove parenthesis around (300 + 10m) 300 + 10m + -1(0.6m2 + -5m + 24) = 0 Reorder the terms: 300 + 10m + -1(24 + -5m + 0.6m2) = 0 300 + 10m + (24 * -1 + -5m * -1 + 0.6m2 * -1) = 0 300 + 10m + (-24 + 5m + -0.6m2) = 0 Reorder the terms: 300 + -24 + 10m + 5m + -0.6m2 = 0 Combine like terms: 300 + -24 = 276 276 + 10m + 5m + -0.6m2 = 0 Combine like terms: 10m + 5m = 15m 276 + 15m + -0.6m2 = 0 Solving 276 + 15m + -0.6m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. -460 + -25m + m2 = 0 Move the constant term to the right: Add '460' to each side of the equation. -460 + -25m + 460 + m2 = 0 + 460 Reorder the terms: -460 + 460 + -25m + m2 = 0 + 460 Combine like terms: -460 + 460 = 0 0 + -25m + m2 = 0 + 460 -25m + m2 = 0 + 460 Combine like terms: 0 + 460 = 460 -25m + m2 = 460 The m term is -25m. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25m + 156.25 + m2 = 460 + 156.25 Reorder the terms: 156.25 + -25m + m2 = 460 + 156.25 Combine like terms: 460 + 156.25 = 616.25 156.25 + -25m + m2 = 616.25 Factor a perfect square on the left side: (m + -12.5)(m + -12.5) = 616.25 Calculate the square root of the right side: 24.824383175 Break this problem into two subproblems by setting (m + -12.5) equal to 24.824383175 and -24.824383175.Subproblem 1
m + -12.5 = 24.824383175 Simplifying m + -12.5 = 24.824383175 Reorder the terms: -12.5 + m = 24.824383175 Solving -12.5 + m = 24.824383175 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + m = 24.824383175 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + m = 24.824383175 + 12.5 m = 24.824383175 + 12.5 Combine like terms: 24.824383175 + 12.5 = 37.324383175 m = 37.324383175 Simplifying m = 37.324383175Subproblem 2
m + -12.5 = -24.824383175 Simplifying m + -12.5 = -24.824383175 Reorder the terms: -12.5 + m = -24.824383175 Solving -12.5 + m = -24.824383175 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + m = -24.824383175 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + m = -24.824383175 + 12.5 m = -24.824383175 + 12.5 Combine like terms: -24.824383175 + 12.5 = -12.324383175 m = -12.324383175 Simplifying m = -12.324383175Solution
The solution to the problem is based on the solutions from the subproblems. m = {37.324383175, -12.324383175}
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