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Simplifying 0 = 2(3r2 + 4r + 2) + -3(-1r2 + 4r + -5) Reorder the terms: 0 = 2(2 + 4r + 3r2) + -3(-1r2 + 4r + -5) 0 = (2 * 2 + 4r * 2 + 3r2 * 2) + -3(-1r2 + 4r + -5) 0 = (4 + 8r + 6r2) + -3(-1r2 + 4r + -5) Reorder the terms: 0 = 4 + 8r + 6r2 + -3(-5 + 4r + -1r2) 0 = 4 + 8r + 6r2 + (-5 * -3 + 4r * -3 + -1r2 * -3) 0 = 4 + 8r + 6r2 + (15 + -12r + 3r2) Reorder the terms: 0 = 4 + 15 + 8r + -12r + 6r2 + 3r2 Combine like terms: 4 + 15 = 19 0 = 19 + 8r + -12r + 6r2 + 3r2 Combine like terms: 8r + -12r = -4r 0 = 19 + -4r + 6r2 + 3r2 Combine like terms: 6r2 + 3r2 = 9r2 0 = 19 + -4r + 9r2 Solving 0 = 19 + -4r + 9r2 Solving for variable 'r'. Combine like terms: 0 + -19 = -19 -19 + 4r + -9r2 = 19 + -4r + 9r2 + -19 + 4r + -9r2 Reorder the terms: -19 + 4r + -9r2 = 19 + -19 + -4r + 4r + 9r2 + -9r2 Combine like terms: 19 + -19 = 0 -19 + 4r + -9r2 = 0 + -4r + 4r + 9r2 + -9r2 -19 + 4r + -9r2 = -4r + 4r + 9r2 + -9r2 Combine like terms: -4r + 4r = 0 -19 + 4r + -9r2 = 0 + 9r2 + -9r2 -19 + 4r + -9r2 = 9r2 + -9r2 Combine like terms: 9r2 + -9r2 = 0 -19 + 4r + -9r2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 2.111111111 + -0.4444444444r + r2 = 0 Move the constant term to the right: Add '-2.111111111' to each side of the equation. 2.111111111 + -0.4444444444r + -2.111111111 + r2 = 0 + -2.111111111 Reorder the terms: 2.111111111 + -2.111111111 + -0.4444444444r + r2 = 0 + -2.111111111 Combine like terms: 2.111111111 + -2.111111111 = 0.000000000 0.000000000 + -0.4444444444r + r2 = 0 + -2.111111111 -0.4444444444r + r2 = 0 + -2.111111111 Combine like terms: 0 + -2.111111111 = -2.111111111 -0.4444444444r + r2 = -2.111111111 The r term is -0.4444444444r. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444r + 0.04938271604 + r2 = -2.111111111 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444r + r2 = -2.111111111 + 0.04938271604 Combine like terms: -2.111111111 + 0.04938271604 = -2.06172839496 0.04938271604 + -0.4444444444r + r2 = -2.06172839496 Factor a perfect square on the left side: (r + -0.2222222222)(r + -0.2222222222) = -2.06172839496 Can't calculate square root of the right side. The solution to this equation could not be determined.
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