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Simplifying (r2 + 3r + 4) + (6r2 + 4r + 5) = 0 Reorder the terms: (4 + 3r + r2) + (6r2 + 4r + 5) = 0 Remove parenthesis around (4 + 3r + r2) 4 + 3r + r2 + (6r2 + 4r + 5) = 0 Reorder the terms: 4 + 3r + r2 + (5 + 4r + 6r2) = 0 Remove parenthesis around (5 + 4r + 6r2) 4 + 3r + r2 + 5 + 4r + 6r2 = 0 Reorder the terms: 4 + 5 + 3r + 4r + r2 + 6r2 = 0 Combine like terms: 4 + 5 = 9 9 + 3r + 4r + r2 + 6r2 = 0 Combine like terms: 3r + 4r = 7r 9 + 7r + r2 + 6r2 = 0 Combine like terms: r2 + 6r2 = 7r2 9 + 7r + 7r2 = 0 Solving 9 + 7r + 7r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.285714286 + r + r2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + r + -1.285714286 + r2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + r + r2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + r + r2 = 0 + -1.285714286 r + r2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 r + r2 = -1.285714286 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + r2 = -1.285714286 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + r2 = -1.285714286 + 0.25 Combine like terms: -1.285714286 + 0.25 = -1.035714286 1.25 + r2 = -1.035714286 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = -1.035714286 Can't calculate square root of the right side. The solution to this equation could not be determined.
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