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Simplifying 5r2 + -44 + 120 = -30 + 11r Reorder the terms: -44 + 120 + 5r2 = -30 + 11r Combine like terms: -44 + 120 = 76 76 + 5r2 = -30 + 11r Solving 76 + 5r2 = -30 + 11r Solving for variable 'r'. Reorder the terms: 76 + 30 + -11r + 5r2 = -30 + 11r + 30 + -11r Combine like terms: 76 + 30 = 106 106 + -11r + 5r2 = -30 + 11r + 30 + -11r Reorder the terms: 106 + -11r + 5r2 = -30 + 30 + 11r + -11r Combine like terms: -30 + 30 = 0 106 + -11r + 5r2 = 0 + 11r + -11r 106 + -11r + 5r2 = 11r + -11r Combine like terms: 11r + -11r = 0 106 + -11r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 21.2 + -2.2r + r2 = 0 Move the constant term to the right: Add '-21.2' to each side of the equation. 21.2 + -2.2r + -21.2 + r2 = 0 + -21.2 Reorder the terms: 21.2 + -21.2 + -2.2r + r2 = 0 + -21.2 Combine like terms: 21.2 + -21.2 = 0.0 0.0 + -2.2r + r2 = 0 + -21.2 -2.2r + r2 = 0 + -21.2 Combine like terms: 0 + -21.2 = -21.2 -2.2r + r2 = -21.2 The r term is -2.2r. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2r + 1.21 + r2 = -21.2 + 1.21 Reorder the terms: 1.21 + -2.2r + r2 = -21.2 + 1.21 Combine like terms: -21.2 + 1.21 = -19.99 1.21 + -2.2r + r2 = -19.99 Factor a perfect square on the left side: (r + -1.1)(r + -1.1) = -19.99 Can't calculate square root of the right side. The solution to this equation could not be determined.
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