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Simplifying 5m + -3m2 + -1(4m2 + -2m + 7) = 0 Reorder the terms: 5m + -3m2 + -1(7 + -2m + 4m2) = 0 5m + -3m2 + (7 * -1 + -2m * -1 + 4m2 * -1) = 0 5m + -3m2 + (-7 + 2m + -4m2) = 0 Reorder the terms: -7 + 5m + 2m + -3m2 + -4m2 = 0 Combine like terms: 5m + 2m = 7m -7 + 7m + -3m2 + -4m2 = 0 Combine like terms: -3m2 + -4m2 = -7m2 -7 + 7m + -7m2 = 0 Solving -7 + 7m + -7m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '7'. 7(-1 + m + -1m2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-1 + m + -1m2)' equal to zero and attempt to solve: Simplifying -1 + m + -1m2 = 0 Solving -1 + m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -1m + m2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + -1m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1m + m2 = 0 + -1 -1m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1m + m2 = -1 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. -1m + 0.25 + m2 = -1 + 0.25 Reorder the terms: 0.25 + -1m + m2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -1m + m2 = -0.75 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = -0.75 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. The solution to this equation could not be determined.
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