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Simplifying 5m + 4 = 7m(m + 1) + 2m Reorder the terms: 4 + 5m = 7m(m + 1) + 2m Reorder the terms: 4 + 5m = 7m(1 + m) + 2m 4 + 5m = (1 * 7m + m * 7m) + 2m 4 + 5m = (7m + 7m2) + 2m Reorder the terms: 4 + 5m = 7m + 2m + 7m2 Combine like terms: 7m + 2m = 9m 4 + 5m = 9m + 7m2 Solving 4 + 5m = 9m + 7m2 Solving for variable 'm'. Combine like terms: 5m + -9m = -4m 4 + -4m + -7m2 = 9m + 7m2 + -9m + -7m2 Reorder the terms: 4 + -4m + -7m2 = 9m + -9m + 7m2 + -7m2 Combine like terms: 9m + -9m = 0 4 + -4m + -7m2 = 0 + 7m2 + -7m2 4 + -4m + -7m2 = 7m2 + -7m2 Combine like terms: 7m2 + -7m2 = 0 4 + -4m + -7m2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.5714285714 + 0.5714285714m + m2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 0.5714285714m + 0.5714285714 + m2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 0.5714285714m + m2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 0.5714285714m + m2 = 0 + 0.5714285714 0.5714285714m + m2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 0.5714285714m + m2 = 0.5714285714 The m term is 0.5714285714m. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714m + 0.08163265305 + m2 = 0.5714285714 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714m + m2 = 0.5714285714 + 0.08163265305 Combine like terms: 0.5714285714 + 0.08163265305 = 0.65306122445 0.08163265305 + 0.5714285714m + m2 = 0.65306122445 Factor a perfect square on the left side: (m + 0.2857142857)(m + 0.2857142857) = 0.65306122445 Calculate the square root of the right side: 0.808122036 Break this problem into two subproblems by setting (m + 0.2857142857) equal to 0.808122036 and -0.808122036.Subproblem 1
m + 0.2857142857 = 0.808122036 Simplifying m + 0.2857142857 = 0.808122036 Reorder the terms: 0.2857142857 + m = 0.808122036 Solving 0.2857142857 + m = 0.808122036 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + m = 0.808122036 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + m = 0.808122036 + -0.2857142857 m = 0.808122036 + -0.2857142857 Combine like terms: 0.808122036 + -0.2857142857 = 0.5224077503 m = 0.5224077503 Simplifying m = 0.5224077503Subproblem 2
m + 0.2857142857 = -0.808122036 Simplifying m + 0.2857142857 = -0.808122036 Reorder the terms: 0.2857142857 + m = -0.808122036 Solving 0.2857142857 + m = -0.808122036 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + m = -0.808122036 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + m = -0.808122036 + -0.2857142857 m = -0.808122036 + -0.2857142857 Combine like terms: -0.808122036 + -0.2857142857 = -1.0938363217 m = -1.0938363217 Simplifying m = -1.0938363217Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.5224077503, -1.0938363217}
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