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Simplifying 3(r + 2 + -5)(4 + -1r + 2) = 12 Reorder the terms: 3(2 + -5 + r)(4 + -1r + 2) = 12 Combine like terms: 2 + -5 = -3 3(-3 + r)(4 + -1r + 2) = 12 Reorder the terms: 3(-3 + r)(4 + 2 + -1r) = 12 Combine like terms: 4 + 2 = 6 3(-3 + r)(6 + -1r) = 12 Multiply (-3 + r) * (6 + -1r) 3(-3(6 + -1r) + r(6 + -1r)) = 12 3((6 * -3 + -1r * -3) + r(6 + -1r)) = 12 3((-18 + 3r) + r(6 + -1r)) = 12 3(-18 + 3r + (6 * r + -1r * r)) = 12 3(-18 + 3r + (6r + -1r2)) = 12 Combine like terms: 3r + 6r = 9r 3(-18 + 9r + -1r2) = 12 (-18 * 3 + 9r * 3 + -1r2 * 3) = 12 (-54 + 27r + -3r2) = 12 Solving -54 + 27r + -3r2 = 12 Solving for variable 'r'. Reorder the terms: -54 + -12 + 27r + -3r2 = 12 + -12 Combine like terms: -54 + -12 = -66 -66 + 27r + -3r2 = 12 + -12 Combine like terms: 12 + -12 = 0 -66 + 27r + -3r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-22 + 9r + -1r2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-22 + 9r + -1r2)' equal to zero and attempt to solve: Simplifying -22 + 9r + -1r2 = 0 Solving -22 + 9r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 22 + -9r + r2 = 0 Move the constant term to the right: Add '-22' to each side of the equation. 22 + -9r + -22 + r2 = 0 + -22 Reorder the terms: 22 + -22 + -9r + r2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -9r + r2 = 0 + -22 -9r + r2 = 0 + -22 Combine like terms: 0 + -22 = -22 -9r + r2 = -22 The r term is -9r. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9r + 20.25 + r2 = -22 + 20.25 Reorder the terms: 20.25 + -9r + r2 = -22 + 20.25 Combine like terms: -22 + 20.25 = -1.75 20.25 + -9r + r2 = -1.75 Factor a perfect square on the left side: (r + -4.5)(r + -4.5) = -1.75 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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