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Simplifying 0 = 16r2 + -23r + 21 Reorder the terms: 0 = 21 + -23r + 16r2 Solving 0 = 21 + -23r + 16r2 Solving for variable 'r'. Combine like terms: 0 + -21 = -21 -21 + 23r + -16r2 = 21 + -23r + 16r2 + -21 + 23r + -16r2 Reorder the terms: -21 + 23r + -16r2 = 21 + -21 + -23r + 23r + 16r2 + -16r2 Combine like terms: 21 + -21 = 0 -21 + 23r + -16r2 = 0 + -23r + 23r + 16r2 + -16r2 -21 + 23r + -16r2 = -23r + 23r + 16r2 + -16r2 Combine like terms: -23r + 23r = 0 -21 + 23r + -16r2 = 0 + 16r2 + -16r2 -21 + 23r + -16r2 = 16r2 + -16r2 Combine like terms: 16r2 + -16r2 = 0 -21 + 23r + -16r2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.3125 + -1.4375r + r2 = 0 Move the constant term to the right: Add '-1.3125' to each side of the equation. 1.3125 + -1.4375r + -1.3125 + r2 = 0 + -1.3125 Reorder the terms: 1.3125 + -1.3125 + -1.4375r + r2 = 0 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + -1.4375r + r2 = 0 + -1.3125 -1.4375r + r2 = 0 + -1.3125 Combine like terms: 0 + -1.3125 = -1.3125 -1.4375r + r2 = -1.3125 The r term is -1.4375r. Take half its coefficient (-0.71875). Square it (0.5166015625) and add it to both sides. Add '0.5166015625' to each side of the equation. -1.4375r + 0.5166015625 + r2 = -1.3125 + 0.5166015625 Reorder the terms: 0.5166015625 + -1.4375r + r2 = -1.3125 + 0.5166015625 Combine like terms: -1.3125 + 0.5166015625 = -0.7958984375 0.5166015625 + -1.4375r + r2 = -0.7958984375 Factor a perfect square on the left side: (r + -0.71875)(r + -0.71875) = -0.7958984375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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