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Simplifying 3m + 1 = 3m2 + 6m + 2 Reorder the terms: 1 + 3m = 3m2 + 6m + 2 Reorder the terms: 1 + 3m = 2 + 6m + 3m2 Solving 1 + 3m = 2 + 6m + 3m2 Solving for variable 'm'. Reorder the terms: 1 + -2 + 3m + -6m + -3m2 = 2 + 6m + 3m2 + -2 + -6m + -3m2 Combine like terms: 1 + -2 = -1 -1 + 3m + -6m + -3m2 = 2 + 6m + 3m2 + -2 + -6m + -3m2 Combine like terms: 3m + -6m = -3m -1 + -3m + -3m2 = 2 + 6m + 3m2 + -2 + -6m + -3m2 Reorder the terms: -1 + -3m + -3m2 = 2 + -2 + 6m + -6m + 3m2 + -3m2 Combine like terms: 2 + -2 = 0 -1 + -3m + -3m2 = 0 + 6m + -6m + 3m2 + -3m2 -1 + -3m + -3m2 = 6m + -6m + 3m2 + -3m2 Combine like terms: 6m + -6m = 0 -1 + -3m + -3m2 = 0 + 3m2 + -3m2 -1 + -3m + -3m2 = 3m2 + -3m2 Combine like terms: 3m2 + -3m2 = 0 -1 + -3m + -3m2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 3m + 3m2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 3m + 3m2)' equal to zero and attempt to solve: Simplifying 1 + 3m + 3m2 = 0 Solving 1 + 3m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + m + m2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + m + -0.3333333333 + m2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + m + m2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + m + m2 = 0 + -0.3333333333 m + m2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 m + m2 = -0.3333333333 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + m2 = -0.3333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 1.25 + m2 = -0.0833333333 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = -0.0833333333 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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