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Simplifying 5.5 + 2r = 36 + r2 Solving 5.5 + 2r = 36 + r2 Solving for variable 'r'. Reorder the terms: 5.5 + -36 + 2r + -1r2 = 36 + r2 + -36 + -1r2 Combine like terms: 5.5 + -36 = -30.5 -30.5 + 2r + -1r2 = 36 + r2 + -36 + -1r2 Reorder the terms: -30.5 + 2r + -1r2 = 36 + -36 + r2 + -1r2 Combine like terms: 36 + -36 = 0 -30.5 + 2r + -1r2 = 0 + r2 + -1r2 -30.5 + 2r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 -30.5 + 2r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 30.5 + -2r + r2 = 0 Move the constant term to the right: Add '-30.5' to each side of the equation. 30.5 + -2r + -30.5 + r2 = 0 + -30.5 Reorder the terms: 30.5 + -30.5 + -2r + r2 = 0 + -30.5 Combine like terms: 30.5 + -30.5 = 0.0 0.0 + -2r + r2 = 0 + -30.5 -2r + r2 = 0 + -30.5 Combine like terms: 0 + -30.5 = -30.5 -2r + r2 = -30.5 The r term is -2r. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2r + 1 + r2 = -30.5 + 1 Reorder the terms: 1 + -2r + r2 = -30.5 + 1 Combine like terms: -30.5 + 1 = -29.5 1 + -2r + r2 = -29.5 Factor a perfect square on the left side: (r + -1)(r + -1) = -29.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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