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Simplifying 5m2 + 2m = 9 Reorder the terms: 2m + 5m2 = 9 Solving 2m + 5m2 = 9 Solving for variable 'm'. Reorder the terms: -9 + 2m + 5m2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 2m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 0.4m + m2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 0.4m + 1.8 + m2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 0.4m + m2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 0.4m + m2 = 0 + 1.8 0.4m + m2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 0.4m + m2 = 1.8 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 = 1.8 + 0.04 Reorder the terms: 0.04 + 0.4m + m2 = 1.8 + 0.04 Combine like terms: 1.8 + 0.04 = 1.84 0.04 + 0.4m + m2 = 1.84 Factor a perfect square on the left side: (m + 0.2)(m + 0.2) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (m + 0.2) equal to 1.356465997 and -1.356465997.Subproblem 1
m + 0.2 = 1.356465997 Simplifying m + 0.2 = 1.356465997 Reorder the terms: 0.2 + m = 1.356465997 Solving 0.2 + m = 1.356465997 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 = 1.356465997 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + m = 1.356465997 + -0.2 m = 1.356465997 + -0.2 Combine like terms: 1.356465997 + -0.2 = 1.156465997 m = 1.156465997 Simplifying m = 1.156465997Subproblem 2
m + 0.2 = -1.356465997 Simplifying m + 0.2 = -1.356465997 Reorder the terms: 0.2 + m = -1.356465997 Solving 0.2 + m = -1.356465997 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 = -1.356465997 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + m = -1.356465997 + -0.2 m = -1.356465997 + -0.2 Combine like terms: -1.356465997 + -0.2 = -1.556465997 m = -1.556465997 Simplifying m = -1.556465997Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.156465997, -1.556465997}
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