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Simplifying 2(-4 + a) = 4a(4 + 2a) (-4 * 2 + a * 2) = 4a(4 + 2a) (-8 + 2a) = 4a(4 + 2a) -8 + 2a = (4 * 4a + 2a * 4a) -8 + 2a = (16a + 8a2) Solving -8 + 2a = 16a + 8a2 Solving for variable 'a'. Combine like terms: 2a + -16a = -14a -8 + -14a + -8a2 = 16a + 8a2 + -16a + -8a2 Reorder the terms: -8 + -14a + -8a2 = 16a + -16a + 8a2 + -8a2 Combine like terms: 16a + -16a = 0 -8 + -14a + -8a2 = 0 + 8a2 + -8a2 -8 + -14a + -8a2 = 8a2 + -8a2 Combine like terms: 8a2 + -8a2 = 0 -8 + -14a + -8a2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + 7a + 4a2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + 7a + 4a2)' equal to zero and attempt to solve: Simplifying 4 + 7a + 4a2 = 0 Solving 4 + 7a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 1.75a + a2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.75a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + 1.75a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.75a + a2 = 0 + -1 1.75a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.75a + a2 = -1 The a term is 1.75a. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75a + 0.765625 + a2 = -1 + 0.765625 Reorder the terms: 0.765625 + 1.75a + a2 = -1 + 0.765625 Combine like terms: -1 + 0.765625 = -0.234375 0.765625 + 1.75a + a2 = -0.234375 Factor a perfect square on the left side: (a + 0.875)(a + 0.875) = -0.234375 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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