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Simplifying 2r + -3 = r2 + 81 Reorder the terms: -3 + 2r = r2 + 81 Reorder the terms: -3 + 2r = 81 + r2 Solving -3 + 2r = 81 + r2 Solving for variable 'r'. Reorder the terms: -3 + -81 + 2r + -1r2 = 81 + r2 + -81 + -1r2 Combine like terms: -3 + -81 = -84 -84 + 2r + -1r2 = 81 + r2 + -81 + -1r2 Reorder the terms: -84 + 2r + -1r2 = 81 + -81 + r2 + -1r2 Combine like terms: 81 + -81 = 0 -84 + 2r + -1r2 = 0 + r2 + -1r2 -84 + 2r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 -84 + 2r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 84 + -2r + r2 = 0 Move the constant term to the right: Add '-84' to each side of the equation. 84 + -2r + -84 + r2 = 0 + -84 Reorder the terms: 84 + -84 + -2r + r2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + -2r + r2 = 0 + -84 -2r + r2 = 0 + -84 Combine like terms: 0 + -84 = -84 -2r + r2 = -84 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 = -84 + 1 Reorder the terms: 1 + -2r + r2 = -84 + 1 Combine like terms: -84 + 1 = -83 1 + -2r + r2 = -83 Factor a perfect square on the left side: (r + -1)(r + -1) = -83 Can't calculate square root of the right side. The solution to this equation could not be determined.
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