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Simplifying -2m(m + 7) + m = 34 Reorder the terms: -2m(7 + m) + m = 34 (7 * -2m + m * -2m) + m = 34 (-14m + -2m2) + m = 34 Reorder the terms: -14m + m + -2m2 = 34 Combine like terms: -14m + m = -13m -13m + -2m2 = 34 Solving -13m + -2m2 = 34 Solving for variable 'm'. Reorder the terms: -34 + -13m + -2m2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + -13m + -2m2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(34 + 13m + 2m2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(34 + 13m + 2m2)' equal to zero and attempt to solve: Simplifying 34 + 13m + 2m2 = 0 Solving 34 + 13m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 17 + 6.5m + m2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + 6.5m + -17 + m2 = 0 + -17 Reorder the terms: 17 + -17 + 6.5m + m2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 6.5m + m2 = 0 + -17 6.5m + m2 = 0 + -17 Combine like terms: 0 + -17 = -17 6.5m + m2 = -17 The m term is 6.5m. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5m + 10.5625 + m2 = -17 + 10.5625 Reorder the terms: 10.5625 + 6.5m + m2 = -17 + 10.5625 Combine like terms: -17 + 10.5625 = -6.4375 10.5625 + 6.5m + m2 = -6.4375 Factor a perfect square on the left side: (m + 3.25)(m + 3.25) = -6.4375 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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