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Simplifying 0 = 2.25x2 + -13x + 20 Reorder the terms: 0 = 20 + -13x + 2.25x2 Solving 0 = 20 + -13x + 2.25x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + 13x + -2.25x2 = 20 + -13x + 2.25x2 + -20 + 13x + -2.25x2 Reorder the terms: -20 + 13x + -2.25x2 = 20 + -20 + -13x + 13x + 2.25x2 + -2.25x2 Combine like terms: 20 + -20 = 0 -20 + 13x + -2.25x2 = 0 + -13x + 13x + 2.25x2 + -2.25x2 -20 + 13x + -2.25x2 = -13x + 13x + 2.25x2 + -2.25x2 Combine like terms: -13x + 13x = 0 -20 + 13x + -2.25x2 = 0 + 2.25x2 + -2.25x2 -20 + 13x + -2.25x2 = 2.25x2 + -2.25x2 Combine like terms: 2.25x2 + -2.25x2 = 0.00 -20 + 13x + -2.25x2 = 0.00 Begin completing the square. Divide all terms by -2.25 the coefficient of the squared term: Divide each side by '-2.25'. 8.888888889 + -5.777777778x + x2 = 0 Move the constant term to the right: Add '-8.888888889' to each side of the equation. 8.888888889 + -5.777777778x + -8.888888889 + x2 = 0 + -8.888888889 Reorder the terms: 8.888888889 + -8.888888889 + -5.777777778x + x2 = 0 + -8.888888889 Combine like terms: 8.888888889 + -8.888888889 = 0.000000000 0.000000000 + -5.777777778x + x2 = 0 + -8.888888889 -5.777777778x + x2 = 0 + -8.888888889 Combine like terms: 0 + -8.888888889 = -8.888888889 -5.777777778x + x2 = -8.888888889 The x term is -5.777777778x. Take half its coefficient (-2.888888889). Square it (8.345679013) and add it to both sides. Add '8.345679013' to each side of the equation. -5.777777778x + 8.345679013 + x2 = -8.888888889 + 8.345679013 Reorder the terms: 8.345679013 + -5.777777778x + x2 = -8.888888889 + 8.345679013 Combine like terms: -8.888888889 + 8.345679013 = -0.543209876 8.345679013 + -5.777777778x + x2 = -0.543209876 Factor a perfect square on the left side: (x + -2.888888889)(x + -2.888888889) = -0.543209876 Can't calculate square root of the right side. The solution to this equation could not be determined.
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