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Simplifying (7a2 + 3a + 14) + (9a2 + 11a) = 0 Reorder the terms: (14 + 3a + 7a2) + (9a2 + 11a) = 0 Remove parenthesis around (14 + 3a + 7a2) 14 + 3a + 7a2 + (9a2 + 11a) = 0 Reorder the terms: 14 + 3a + 7a2 + (11a + 9a2) = 0 Remove parenthesis around (11a + 9a2) 14 + 3a + 7a2 + 11a + 9a2 = 0 Reorder the terms: 14 + 3a + 11a + 7a2 + 9a2 = 0 Combine like terms: 3a + 11a = 14a 14 + 14a + 7a2 + 9a2 = 0 Combine like terms: 7a2 + 9a2 = 16a2 14 + 14a + 16a2 = 0 Solving 14 + 14a + 16a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 7a + 8a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 7a + 8a2)' equal to zero and attempt to solve: Simplifying 7 + 7a + 8a2 = 0 Solving 7 + 7a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + 0.875a + a2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + 0.875a + -0.875 + a2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + 0.875a + a2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + 0.875a + a2 = 0 + -0.875 0.875a + a2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 0.875a + a2 = -0.875 The a term is 0.875a. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875a + 0.19140625 + a2 = -0.875 + 0.19140625 Reorder the terms: 0.19140625 + 0.875a + a2 = -0.875 + 0.19140625 Combine like terms: -0.875 + 0.19140625 = -0.68359375 0.19140625 + 0.875a + a2 = -0.68359375 Factor a perfect square on the left side: (a + 0.4375)(a + 0.4375) = -0.68359375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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