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Simplifying 2m2(5m2 + -9m + 2) = 0 Reorder the terms: 2m2(2 + -9m + 5m2) = 0 (2 * 2m2 + -9m * 2m2 + 5m2 * 2m2) = 0 (4m2 + -18m3 + 10m4) = 0 Solving 4m2 + -18m3 + 10m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2m2'. 2m2(2 + -9m + 5m2) = 0 Ignore the factor 2.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 + -9m + 5m2)' equal to zero and attempt to solve: Simplifying 2 + -9m + 5m2 = 0 Solving 2 + -9m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -1.8m + m2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -1.8m + -0.4 + m2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -1.8m + m2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -1.8m + m2 = 0 + -0.4 -1.8m + m2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -1.8m + m2 = -0.4 The m term is -1.8m. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8m + 0.81 + m2 = -0.4 + 0.81 Reorder the terms: 0.81 + -1.8m + m2 = -0.4 + 0.81 Combine like terms: -0.4 + 0.81 = 0.41 0.81 + -1.8m + m2 = 0.41 Factor a perfect square on the left side: (m + -0.9)(m + -0.9) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (m + -0.9) equal to 0.640312424 and -0.640312424.Subproblem 1
m + -0.9 = 0.640312424 Simplifying m + -0.9 = 0.640312424 Reorder the terms: -0.9 + m = 0.640312424 Solving -0.9 + m = 0.640312424 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + m = 0.640312424 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + m = 0.640312424 + 0.9 m = 0.640312424 + 0.9 Combine like terms: 0.640312424 + 0.9 = 1.540312424 m = 1.540312424 Simplifying m = 1.540312424Subproblem 2
m + -0.9 = -0.640312424 Simplifying m + -0.9 = -0.640312424 Reorder the terms: -0.9 + m = -0.640312424 Solving -0.9 + m = -0.640312424 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + m = -0.640312424 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + m = -0.640312424 + 0.9 m = -0.640312424 + 0.9 Combine like terms: -0.640312424 + 0.9 = 0.259687576 m = 0.259687576 Simplifying m = 0.259687576Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.540312424, 0.259687576}Solution
m = {0, 1.540312424, 0.259687576}
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