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Simplifying 7 + 8 + -5r = 2r(4 + -2r) Combine like terms: 7 + 8 = 15 15 + -5r = 2r(4 + -2r) 15 + -5r = (4 * 2r + -2r * 2r) 15 + -5r = (8r + -4r2) Solving 15 + -5r = 8r + -4r2 Solving for variable 'r'. Combine like terms: -5r + -8r = -13r 15 + -13r + 4r2 = 8r + -4r2 + -8r + 4r2 Reorder the terms: 15 + -13r + 4r2 = 8r + -8r + -4r2 + 4r2 Combine like terms: 8r + -8r = 0 15 + -13r + 4r2 = 0 + -4r2 + 4r2 15 + -13r + 4r2 = -4r2 + 4r2 Combine like terms: -4r2 + 4r2 = 0 15 + -13r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -3.25r + r2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -3.25r + -3.75 + r2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -3.25r + r2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -3.25r + r2 = 0 + -3.75 -3.25r + r2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -3.25r + r2 = -3.75 The r term is -3.25r. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25r + 2.640625 + r2 = -3.75 + 2.640625 Reorder the terms: 2.640625 + -3.25r + r2 = -3.75 + 2.640625 Combine like terms: -3.75 + 2.640625 = -1.109375 2.640625 + -3.25r + r2 = -1.109375 Factor a perfect square on the left side: (r + -1.625)(r + -1.625) = -1.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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