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Simplifying (a2 + a + 1) + (5a2 + -8a + 20) = 0 Reorder the terms: (1 + a + a2) + (5a2 + -8a + 20) = 0 Remove parenthesis around (1 + a + a2) 1 + a + a2 + (5a2 + -8a + 20) = 0 Reorder the terms: 1 + a + a2 + (20 + -8a + 5a2) = 0 Remove parenthesis around (20 + -8a + 5a2) 1 + a + a2 + 20 + -8a + 5a2 = 0 Reorder the terms: 1 + 20 + a + -8a + a2 + 5a2 = 0 Combine like terms: 1 + 20 = 21 21 + a + -8a + a2 + 5a2 = 0 Combine like terms: a + -8a = -7a 21 + -7a + a2 + 5a2 = 0 Combine like terms: a2 + 5a2 = 6a2 21 + -7a + 6a2 = 0 Solving 21 + -7a + 6a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.5 + -1.166666667a + a2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -1.166666667a + -3.5 + a2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -1.166666667a + a2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -1.166666667a + a2 = 0 + -3.5 -1.166666667a + a2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -1.166666667a + a2 = -3.5 The a term is -1.166666667a. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667a + 0.3402777780 + a2 = -3.5 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667a + a2 = -3.5 + 0.3402777780 Combine like terms: -3.5 + 0.3402777780 = -3.159722222 0.3402777780 + -1.166666667a + a2 = -3.159722222 Factor a perfect square on the left side: (a + -0.5833333335)(a + -0.5833333335) = -3.159722222 Can't calculate square root of the right side. The solution to this equation could not be determined.
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