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Simplifying -4a2 + -1 = 3a Reorder the terms: -1 + -4a2 = 3a Solving -1 + -4a2 = 3a Solving for variable 'a'. Reorder the terms: -1 + -3a + -4a2 = 3a + -3a Combine like terms: 3a + -3a = 0 -1 + -3a + -4a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 3a + 4a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 3a + 4a2)' equal to zero and attempt to solve: Simplifying 1 + 3a + 4a2 = 0 Solving 1 + 3a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 0.75a + a2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 0.75a + -0.25 + a2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 0.75a + a2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 0.75a + a2 = 0 + -0.25 0.75a + a2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 0.75a + a2 = -0.25 The a term is 0.75a. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75a + 0.140625 + a2 = -0.25 + 0.140625 Reorder the terms: 0.140625 + 0.75a + a2 = -0.25 + 0.140625 Combine like terms: -0.25 + 0.140625 = -0.109375 0.140625 + 0.75a + a2 = -0.109375 Factor a perfect square on the left side: (a + 0.375)(a + 0.375) = -0.109375 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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