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Simplifying 5a2 + -6a + 7a2 + 3a + -2 + 8a + 7 = 0 Reorder the terms: -2 + 7 + -6a + 3a + 8a + 5a2 + 7a2 = 0 Combine like terms: -2 + 7 = 5 5 + -6a + 3a + 8a + 5a2 + 7a2 = 0 Combine like terms: -6a + 3a = -3a 5 + -3a + 8a + 5a2 + 7a2 = 0 Combine like terms: -3a + 8a = 5a 5 + 5a + 5a2 + 7a2 = 0 Combine like terms: 5a2 + 7a2 = 12a2 5 + 5a + 12a2 = 0 Solving 5 + 5a + 12a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + 0.4166666667a + a2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + 0.4166666667a + -0.4166666667 + a2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + 0.4166666667a + a2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + 0.4166666667a + a2 = 0 + -0.4166666667 0.4166666667a + a2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 0.4166666667a + a2 = -0.4166666667 The a term is 0.4166666667a. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667a + 0.04340277781 + a2 = -0.4166666667 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667a + a2 = -0.4166666667 + 0.04340277781 Combine like terms: -0.4166666667 + 0.04340277781 = -0.37326388889 0.04340277781 + 0.4166666667a + a2 = -0.37326388889 Factor a perfect square on the left side: (a + 0.2083333334)(a + 0.2083333334) = -0.37326388889 Can't calculate square root of the right side. The solution to this equation could not be determined.
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