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Simplifying 2r(5 + -1r) = 13 + 2r (5 * 2r + -1r * 2r) = 13 + 2r (10r + -2r2) = 13 + 2r Solving 10r + -2r2 = 13 + 2r Solving for variable 'r'. Reorder the terms: -13 + 10r + -2r + -2r2 = 13 + 2r + -13 + -2r Combine like terms: 10r + -2r = 8r -13 + 8r + -2r2 = 13 + 2r + -13 + -2r Reorder the terms: -13 + 8r + -2r2 = 13 + -13 + 2r + -2r Combine like terms: 13 + -13 = 0 -13 + 8r + -2r2 = 0 + 2r + -2r -13 + 8r + -2r2 = 2r + -2r Combine like terms: 2r + -2r = 0 -13 + 8r + -2r2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 6.5 + -4r + r2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -4r + -6.5 + r2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -4r + r2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -4r + r2 = 0 + -6.5 -4r + r2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -4r + r2 = -6.5 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = -6.5 + 4 Reorder the terms: 4 + -4r + r2 = -6.5 + 4 Combine like terms: -6.5 + 4 = -2.5 4 + -4r + r2 = -2.5 Factor a perfect square on the left side: (r + -2)(r + -2) = -2.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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