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Simplifying 4a2 + 12a + 14 = 0 Reorder the terms: 14 + 12a + 4a2 = 0 Solving 14 + 12a + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 6a + 2a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 6a + 2a2)' equal to zero and attempt to solve: Simplifying 7 + 6a + 2a2 = 0 Solving 7 + 6a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 3a + a2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 3a + -3.5 + a2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 3a + a2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 3a + a2 = 0 + -3.5 3a + a2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 3a + a2 = -3.5 The a term is 3a. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3a + 2.25 + a2 = -3.5 + 2.25 Reorder the terms: 2.25 + 3a + a2 = -3.5 + 2.25 Combine like terms: -3.5 + 2.25 = -1.25 2.25 + 3a + a2 = -1.25 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = -1.25 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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