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Simplifying 2r2 + -3r + 9 = 0 Reorder the terms: 9 + -3r + 2r2 = 0 Solving 9 + -3r + 2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -1.5r + r2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -1.5r + -4.5 + r2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -1.5r + r2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -1.5r + r2 = 0 + -4.5 -1.5r + r2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -1.5r + r2 = -4.5 The r term is -1.5r. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5r + 0.5625 + r2 = -4.5 + 0.5625 Reorder the terms: 0.5625 + -1.5r + r2 = -4.5 + 0.5625 Combine like terms: -4.5 + 0.5625 = -3.9375 0.5625 + -1.5r + r2 = -3.9375 Factor a perfect square on the left side: (r + -0.75)(r + -0.75) = -3.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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