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Simplifying 100 + -1(6m + 7)(12m + 16) = 109 Reorder the terms: 100 + -1(7 + 6m)(12m + 16) = 109 Reorder the terms: 100 + -1(7 + 6m)(16 + 12m) = 109 Multiply (7 + 6m) * (16 + 12m) 100 + -1(7(16 + 12m) + 6m * (16 + 12m)) = 109 100 + -1((16 * 7 + 12m * 7) + 6m * (16 + 12m)) = 109 100 + -1((112 + 84m) + 6m * (16 + 12m)) = 109 100 + -1(112 + 84m + (16 * 6m + 12m * 6m)) = 109 100 + -1(112 + 84m + (96m + 72m2)) = 109 Combine like terms: 84m + 96m = 180m 100 + -1(112 + 180m + 72m2) = 109 100 + (112 * -1 + 180m * -1 + 72m2 * -1) = 109 100 + (-112 + -180m + -72m2) = 109 Combine like terms: 100 + -112 = -12 -12 + -180m + -72m2 = 109 Solving -12 + -180m + -72m2 = 109 Solving for variable 'm'. Reorder the terms: -12 + -109 + -180m + -72m2 = 109 + -109 Combine like terms: -12 + -109 = -121 -121 + -180m + -72m2 = 109 + -109 Combine like terms: 109 + -109 = 0 -121 + -180m + -72m2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(121 + 180m + 72m2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(121 + 180m + 72m2)' equal to zero and attempt to solve: Simplifying 121 + 180m + 72m2 = 0 Solving 121 + 180m + 72m2 = 0 Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. 1.680555556 + 2.5m + m2 = 0 Move the constant term to the right: Add '-1.680555556' to each side of the equation. 1.680555556 + 2.5m + -1.680555556 + m2 = 0 + -1.680555556 Reorder the terms: 1.680555556 + -1.680555556 + 2.5m + m2 = 0 + -1.680555556 Combine like terms: 1.680555556 + -1.680555556 = 0.000000000 0.000000000 + 2.5m + m2 = 0 + -1.680555556 2.5m + m2 = 0 + -1.680555556 Combine like terms: 0 + -1.680555556 = -1.680555556 2.5m + m2 = -1.680555556 The m term is 2.5m. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5m + 1.5625 + m2 = -1.680555556 + 1.5625 Reorder the terms: 1.5625 + 2.5m + m2 = -1.680555556 + 1.5625 Combine like terms: -1.680555556 + 1.5625 = -0.118055556 1.5625 + 2.5m + m2 = -0.118055556 Factor a perfect square on the left side: (m + 1.25)(m + 1.25) = -0.118055556 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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