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Simplifying (4m2 + 9m) + -1(-3m2 + -4m + 9) = 0 Reorder the terms: (9m + 4m2) + -1(-3m2 + -4m + 9) = 0 Remove parenthesis around (9m + 4m2) 9m + 4m2 + -1(-3m2 + -4m + 9) = 0 Reorder the terms: 9m + 4m2 + -1(9 + -4m + -3m2) = 0 9m + 4m2 + (9 * -1 + -4m * -1 + -3m2 * -1) = 0 9m + 4m2 + (-9 + 4m + 3m2) = 0 Reorder the terms: -9 + 9m + 4m + 4m2 + 3m2 = 0 Combine like terms: 9m + 4m = 13m -9 + 13m + 4m2 + 3m2 = 0 Combine like terms: 4m2 + 3m2 = 7m2 -9 + 13m + 7m2 = 0 Solving -9 + 13m + 7m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + 1.857142857m + m2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 1.857142857m + 1.285714286 + m2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 1.857142857m + m2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 1.857142857m + m2 = 0 + 1.285714286 1.857142857m + m2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 1.857142857m + m2 = 1.285714286 The m term is 1.857142857m. Take half its coefficient (0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. 1.857142857m + 0.8622448978 + m2 = 1.285714286 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857m + m2 = 1.285714286 + 0.8622448978 Combine like terms: 1.285714286 + 0.8622448978 = 2.1479591838 0.8622448978 + 1.857142857m + m2 = 2.1479591838 Factor a perfect square on the left side: (m + 0.9285714285)(m + 0.9285714285) = 2.1479591838 Calculate the square root of the right side: 1.465591752 Break this problem into two subproblems by setting (m + 0.9285714285) equal to 1.465591752 and -1.465591752.Subproblem 1
m + 0.9285714285 = 1.465591752 Simplifying m + 0.9285714285 = 1.465591752 Reorder the terms: 0.9285714285 + m = 1.465591752 Solving 0.9285714285 + m = 1.465591752 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + m = 1.465591752 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + m = 1.465591752 + -0.9285714285 m = 1.465591752 + -0.9285714285 Combine like terms: 1.465591752 + -0.9285714285 = 0.5370203235 m = 0.5370203235 Simplifying m = 0.5370203235Subproblem 2
m + 0.9285714285 = -1.465591752 Simplifying m + 0.9285714285 = -1.465591752 Reorder the terms: 0.9285714285 + m = -1.465591752 Solving 0.9285714285 + m = -1.465591752 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + m = -1.465591752 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + m = -1.465591752 + -0.9285714285 m = -1.465591752 + -0.9285714285 Combine like terms: -1.465591752 + -0.9285714285 = -2.3941631805 m = -2.3941631805 Simplifying m = -2.3941631805Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.5370203235, -2.3941631805}
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