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Simplifying 0 = 3m3 + -21m2 + 75m Reorder the terms: 0 = 75m + -21m2 + 3m3 Solving 0 = 75m + -21m2 + 3m3 Solving for variable 'm'. Remove the zero: -75m + 21m2 + -3m3 = 75m + -21m2 + 3m3 + -75m + 21m2 + -3m3 Reorder the terms: -75m + 21m2 + -3m3 = 75m + -75m + -21m2 + 21m2 + 3m3 + -3m3 Combine like terms: 75m + -75m = 0 -75m + 21m2 + -3m3 = 0 + -21m2 + 21m2 + 3m3 + -3m3 -75m + 21m2 + -3m3 = -21m2 + 21m2 + 3m3 + -3m3 Combine like terms: -21m2 + 21m2 = 0 -75m + 21m2 + -3m3 = 0 + 3m3 + -3m3 -75m + 21m2 + -3m3 = 3m3 + -3m3 Combine like terms: 3m3 + -3m3 = 0 -75m + 21m2 + -3m3 = 0 Factor out the Greatest Common Factor (GCF), '3m'. 3m(-25 + 7m + -1m2) = 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 '(-25 + 7m + -1m2)' equal to zero and attempt to solve: Simplifying -25 + 7m + -1m2 = 0 Solving -25 + 7m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -7m + m2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -7m + -25 + m2 = 0 + -25 Reorder the terms: 25 + -25 + -7m + m2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -7m + m2 = 0 + -25 -7m + m2 = 0 + -25 Combine like terms: 0 + -25 = -25 -7m + m2 = -25 The m term is -7m. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7m + 12.25 + m2 = -25 + 12.25 Reorder the terms: 12.25 + -7m + m2 = -25 + 12.25 Combine like terms: -25 + 12.25 = -12.75 12.25 + -7m + m2 = -12.75 Factor a perfect square on the left side: (m + -3.5)(m + -3.5) = -12.75 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.Solution
m = {0}
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