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Simplifying 2r(5 + -1r) = 13 + 3r (5 * 2r + -1r * 2r) = 13 + 3r (10r + -2r2) = 13 + 3r Solving 10r + -2r2 = 13 + 3r Solving for variable 'r'. Reorder the terms: -13 + 10r + -3r + -2r2 = 13 + 3r + -13 + -3r Combine like terms: 10r + -3r = 7r -13 + 7r + -2r2 = 13 + 3r + -13 + -3r Reorder the terms: -13 + 7r + -2r2 = 13 + -13 + 3r + -3r Combine like terms: 13 + -13 = 0 -13 + 7r + -2r2 = 0 + 3r + -3r -13 + 7r + -2r2 = 3r + -3r Combine like terms: 3r + -3r = 0 -13 + 7r + -2r2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 6.5 + -3.5r + r2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -3.5r + -6.5 + r2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -3.5r + r2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -3.5r + r2 = 0 + -6.5 -3.5r + r2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -3.5r + r2 = -6.5 The r term is -3.5r. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5r + 3.0625 + r2 = -6.5 + 3.0625 Reorder the terms: 3.0625 + -3.5r + r2 = -6.5 + 3.0625 Combine like terms: -6.5 + 3.0625 = -3.4375 3.0625 + -3.5r + r2 = -3.4375 Factor a perfect square on the left side: (r + -1.75)(r + -1.75) = -3.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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