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Simplifying 4m2 + -227m + -40 = 0 Reorder the terms: -40 + -227m + 4m2 = 0 Solving -40 + -227m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10 + -56.75m + m2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -56.75m + 10 + m2 = 0 + 10 Reorder the terms: -10 + 10 + -56.75m + m2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -56.75m + m2 = 0 + 10 -56.75m + m2 = 0 + 10 Combine like terms: 0 + 10 = 10 -56.75m + m2 = 10 The m term is -56.75m. Take half its coefficient (-28.375). Square it (805.140625) and add it to both sides. Add '805.140625' to each side of the equation. -56.75m + 805.140625 + m2 = 10 + 805.140625 Reorder the terms: 805.140625 + -56.75m + m2 = 10 + 805.140625 Combine like terms: 10 + 805.140625 = 815.140625 805.140625 + -56.75m + m2 = 815.140625 Factor a perfect square on the left side: (m + -28.375)(m + -28.375) = 815.140625 Calculate the square root of the right side: 28.55066768 Break this problem into two subproblems by setting (m + -28.375) equal to 28.55066768 and -28.55066768.Subproblem 1
m + -28.375 = 28.55066768 Simplifying m + -28.375 = 28.55066768 Reorder the terms: -28.375 + m = 28.55066768 Solving -28.375 + m = 28.55066768 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '28.375' to each side of the equation. -28.375 + 28.375 + m = 28.55066768 + 28.375 Combine like terms: -28.375 + 28.375 = 0.000 0.000 + m = 28.55066768 + 28.375 m = 28.55066768 + 28.375 Combine like terms: 28.55066768 + 28.375 = 56.92566768 m = 56.92566768 Simplifying m = 56.92566768Subproblem 2
m + -28.375 = -28.55066768 Simplifying m + -28.375 = -28.55066768 Reorder the terms: -28.375 + m = -28.55066768 Solving -28.375 + m = -28.55066768 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '28.375' to each side of the equation. -28.375 + 28.375 + m = -28.55066768 + 28.375 Combine like terms: -28.375 + 28.375 = 0.000 0.000 + m = -28.55066768 + 28.375 m = -28.55066768 + 28.375 Combine like terms: -28.55066768 + 28.375 = -0.17566768 m = -0.17566768 Simplifying m = -0.17566768Solution
The solution to the problem is based on the solutions from the subproblems. m = {56.92566768, -0.17566768}
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