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Simplifying 5r2 + -44r + 120 = -50 + 11r Reorder the terms: 120 + -44r + 5r2 = -50 + 11r Solving 120 + -44r + 5r2 = -50 + 11r Solving for variable 'r'. Reorder the terms: 120 + 50 + -44r + -11r + 5r2 = -50 + 11r + 50 + -11r Combine like terms: 120 + 50 = 170 170 + -44r + -11r + 5r2 = -50 + 11r + 50 + -11r Combine like terms: -44r + -11r = -55r 170 + -55r + 5r2 = -50 + 11r + 50 + -11r Reorder the terms: 170 + -55r + 5r2 = -50 + 50 + 11r + -11r Combine like terms: -50 + 50 = 0 170 + -55r + 5r2 = 0 + 11r + -11r 170 + -55r + 5r2 = 11r + -11r Combine like terms: 11r + -11r = 0 170 + -55r + 5r2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(34 + -11r + r2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(34 + -11r + r2)' equal to zero and attempt to solve: Simplifying 34 + -11r + r2 = 0 Solving 34 + -11r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -11r + -34 + r2 = 0 + -34 Reorder the terms: 34 + -34 + -11r + r2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -11r + r2 = 0 + -34 -11r + r2 = 0 + -34 Combine like terms: 0 + -34 = -34 -11r + r2 = -34 The r term is -11r. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11r + 30.25 + r2 = -34 + 30.25 Reorder the terms: 30.25 + -11r + r2 = -34 + 30.25 Combine like terms: -34 + 30.25 = -3.75 30.25 + -11r + r2 = -3.75 Factor a perfect square on the left side: (r + -5.5)(r + -5.5) = -3.75 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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