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Simplifying 28m4 + 40m3 + 8m2 = 0 Reorder the terms: 8m2 + 40m3 + 28m4 = 0 Solving 8m2 + 40m3 + 28m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '4m2'. 4m2(2 + 10m + 7m2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'm2' equal to zero and attempt to solve: Simplifying m2 = 0 Solving m2 = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m2 = 0 Take the square root of each side: m = {0}Subproblem 2
Set the factor '(2 + 10m + 7m2)' equal to zero and attempt to solve: Simplifying 2 + 10m + 7m2 = 0 Solving 2 + 10m + 7m2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + 1.428571429m + m2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 1.428571429m + -0.2857142857 + m2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 1.428571429m + m2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 1.428571429m + m2 = 0 + -0.2857142857 1.428571429m + m2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 1.428571429m + m2 = -0.2857142857 The m term is 1.428571429m. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429m + 0.5102040819 + m2 = -0.2857142857 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429m + m2 = -0.2857142857 + 0.5102040819 Combine like terms: -0.2857142857 + 0.5102040819 = 0.2244897962 0.5102040819 + 1.428571429m + m2 = 0.2244897962 Factor a perfect square on the left side: (m + 0.7142857145)(m + 0.7142857145) = 0.2244897962 Calculate the square root of the right side: 0.473803542 Break this problem into two subproblems by setting (m + 0.7142857145) equal to 0.473803542 and -0.473803542.Subproblem 1
m + 0.7142857145 = 0.473803542 Simplifying m + 0.7142857145 = 0.473803542 Reorder the terms: 0.7142857145 + m = 0.473803542 Solving 0.7142857145 + m = 0.473803542 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + m = 0.473803542 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + m = 0.473803542 + -0.7142857145 m = 0.473803542 + -0.7142857145 Combine like terms: 0.473803542 + -0.7142857145 = -0.2404821725 m = -0.2404821725 Simplifying m = -0.2404821725Subproblem 2
m + 0.7142857145 = -0.473803542 Simplifying m + 0.7142857145 = -0.473803542 Reorder the terms: 0.7142857145 + m = -0.473803542 Solving 0.7142857145 + m = -0.473803542 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + m = -0.473803542 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + m = -0.473803542 + -0.7142857145 m = -0.473803542 + -0.7142857145 Combine like terms: -0.473803542 + -0.7142857145 = -1.1880892565 m = -1.1880892565 Simplifying m = -1.1880892565Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.2404821725, -1.1880892565}Solution
m = {0, -0.2404821725, -1.1880892565}
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