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Simplifying 0.5(4r2 + -10r) + -1r + 5 = 0 Reorder the terms: 0.5(-10r + 4r2) + -1r + 5 = 0 (-10r * 0.5 + 4r2 * 0.5) + -1r + 5 = 0 (-5r + 2r2) + -1r + 5 = 0 Reorder the terms: 5 + -5r + -1r + 2r2 = 0 Combine like terms: -5r + -1r = -6r 5 + -6r + 2r2 = 0 Solving 5 + -6r + 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'. 2.5 + -3r + r2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -3r + -2.5 + r2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -3r + r2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -3r + r2 = 0 + -2.5 -3r + r2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -3r + r2 = -2.5 The r term is -3r. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3r + 2.25 + r2 = -2.5 + 2.25 Reorder the terms: 2.25 + -3r + r2 = -2.5 + 2.25 Combine like terms: -2.5 + 2.25 = -0.25 2.25 + -3r + r2 = -0.25 Factor a perfect square on the left side: (r + -1.5)(r + -1.5) = -0.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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