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Simplifying -3m3 + -5m2 + m = 0 Reorder the terms: m + -5m2 + -3m3 = 0 Solving m + -5m2 + -3m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm'. m(1 + -5m + -3m2) = 0Subproblem 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 '(1 + -5m + -3m2)' equal to zero and attempt to solve: Simplifying 1 + -5m + -3m2 = 0 Solving 1 + -5m + -3m2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.3333333333 + 1.666666667m + m2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.666666667m + 0.3333333333 + m2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.666666667m + m2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.666666667m + m2 = 0 + 0.3333333333 1.666666667m + m2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.666666667m + m2 = 0.3333333333 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 = 0.3333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667m + m2 = 0.3333333333 + 0.6944444447 Combine like terms: 0.3333333333 + 0.6944444447 = 1.027777778 0.6944444447 + 1.666666667m + m2 = 1.027777778 Factor a perfect square on the left side: (m + 0.8333333335)(m + 0.8333333335) = 1.027777778 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (m + 0.8333333335) equal to 1.013793755 and -1.013793755.Subproblem 1
m + 0.8333333335 = 1.013793755 Simplifying m + 0.8333333335 = 1.013793755 Reorder the terms: 0.8333333335 + m = 1.013793755 Solving 0.8333333335 + m = 1.013793755 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 = 1.013793755 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + m = 1.013793755 + -0.8333333335 m = 1.013793755 + -0.8333333335 Combine like terms: 1.013793755 + -0.8333333335 = 0.1804604215 m = 0.1804604215 Simplifying m = 0.1804604215Subproblem 2
m + 0.8333333335 = -1.013793755 Simplifying m + 0.8333333335 = -1.013793755 Reorder the terms: 0.8333333335 + m = -1.013793755 Solving 0.8333333335 + m = -1.013793755 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 = -1.013793755 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + m = -1.013793755 + -0.8333333335 m = -1.013793755 + -0.8333333335 Combine like terms: -1.013793755 + -0.8333333335 = -1.8471270885 m = -1.8471270885 Simplifying m = -1.8471270885Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.1804604215, -1.8471270885}Solution
m = {0, 0.1804604215, -1.8471270885}
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