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Simplifying 2(3 + m) * 3m = 9(5m + -10) Reorder the terms for easier multiplication: 2 * 3m(3 + m) = 9(5m + -10) Multiply 2 * 3 6m(3 + m) = 9(5m + -10) (3 * 6m + m * 6m) = 9(5m + -10) (18m + 6m2) = 9(5m + -10) Reorder the terms: 18m + 6m2 = 9(-10 + 5m) 18m + 6m2 = (-10 * 9 + 5m * 9) 18m + 6m2 = (-90 + 45m) Solving 18m + 6m2 = -90 + 45m Solving for variable 'm'. Reorder the terms: 90 + 18m + -45m + 6m2 = -90 + 45m + 90 + -45m Combine like terms: 18m + -45m = -27m 90 + -27m + 6m2 = -90 + 45m + 90 + -45m Reorder the terms: 90 + -27m + 6m2 = -90 + 90 + 45m + -45m Combine like terms: -90 + 90 = 0 90 + -27m + 6m2 = 0 + 45m + -45m 90 + -27m + 6m2 = 45m + -45m Combine like terms: 45m + -45m = 0 90 + -27m + 6m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(30 + -9m + 2m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(30 + -9m + 2m2)' equal to zero and attempt to solve: Simplifying 30 + -9m + 2m2 = 0 Solving 30 + -9m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 15 + -4.5m + m2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -4.5m + -15 + m2 = 0 + -15 Reorder the terms: 15 + -15 + -4.5m + m2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -4.5m + m2 = 0 + -15 -4.5m + m2 = 0 + -15 Combine like terms: 0 + -15 = -15 -4.5m + m2 = -15 The m term is -4.5m. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5m + 5.0625 + m2 = -15 + 5.0625 Reorder the terms: 5.0625 + -4.5m + m2 = -15 + 5.0625 Combine like terms: -15 + 5.0625 = -9.9375 5.0625 + -4.5m + m2 = -9.9375 Factor a perfect square on the left side: (m + -2.25)(m + -2.25) = -9.9375 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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