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Simplifying 9m3 + 15m2 + -21m = 0 Reorder the terms: -21m + 15m2 + 9m3 = 0 Solving -21m + 15m2 + 9m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3m'. 3m(-7 + 5m + 3m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'm' equal to zero and attempt to solve: Simplifying m = 0 Solving m = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m = 0Subproblem 2
Set the factor '(-7 + 5m + 3m2)' equal to zero and attempt to solve: Simplifying -7 + 5m + 3m2 = 0 Solving -7 + 5m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + 1.666666667m + m2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 1.666666667m + 2.333333333 + m2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 1.666666667m + m2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 1.666666667m + m2 = 0 + 2.333333333 1.666666667m + m2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 1.666666667m + m2 = 2.333333333 The m term is 1.666666667m. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667m + 0.6944444447 + m2 = 2.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667m + m2 = 2.333333333 + 0.6944444447 Combine like terms: 2.333333333 + 0.6944444447 = 3.0277777777 0.6944444447 + 1.666666667m + m2 = 3.0277777777 Factor a perfect square on the left side: (m + 0.8333333335)(m + 0.8333333335) = 3.0277777777 Calculate the square root of the right side: 1.740051085 Break this problem into two subproblems by setting (m + 0.8333333335) equal to 1.740051085 and -1.740051085.Subproblem 1
m + 0.8333333335 = 1.740051085 Simplifying m + 0.8333333335 = 1.740051085 Reorder the terms: 0.8333333335 + m = 1.740051085 Solving 0.8333333335 + m = 1.740051085 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + m = 1.740051085 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + m = 1.740051085 + -0.8333333335 m = 1.740051085 + -0.8333333335 Combine like terms: 1.740051085 + -0.8333333335 = 0.9067177515 m = 0.9067177515 Simplifying m = 0.9067177515Subproblem 2
m + 0.8333333335 = -1.740051085 Simplifying m + 0.8333333335 = -1.740051085 Reorder the terms: 0.8333333335 + m = -1.740051085 Solving 0.8333333335 + m = -1.740051085 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + m = -1.740051085 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + m = -1.740051085 + -0.8333333335 m = -1.740051085 + -0.8333333335 Combine like terms: -1.740051085 + -0.8333333335 = -2.5733844185 m = -2.5733844185 Simplifying m = -2.5733844185Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.9067177515, -2.5733844185}Solution
m = {0, 0.9067177515, -2.5733844185}
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