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Simplifying 5r2 + -44r + 120 = -30r + 11r Reorder the terms: 120 + -44r + 5r2 = -30r + 11r Combine like terms: -30r + 11r = -19r 120 + -44r + 5r2 = -19r Solving 120 + -44r + 5r2 = -19r Solving for variable 'r'. Reorder the terms: 120 + -44r + 19r + 5r2 = -19r + 19r Combine like terms: -44r + 19r = -25r 120 + -25r + 5r2 = -19r + 19r Combine like terms: -19r + 19r = 0 120 + -25r + 5r2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(24 + -5r + r2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(24 + -5r + r2)' equal to zero and attempt to solve: Simplifying 24 + -5r + r2 = 0 Solving 24 + -5r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -5r + -24 + r2 = 0 + -24 Reorder the terms: 24 + -24 + -5r + r2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -5r + r2 = 0 + -24 -5r + r2 = 0 + -24 Combine like terms: 0 + -24 = -24 -5r + r2 = -24 The r term is -5r. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5r + 6.25 + r2 = -24 + 6.25 Reorder the terms: 6.25 + -5r + r2 = -24 + 6.25 Combine like terms: -24 + 6.25 = -17.75 6.25 + -5r + r2 = -17.75 Factor a perfect square on the left side: (r + -2.5)(r + -2.5) = -17.75 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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