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Simplifying 4(a + -1) = 6a(3a + 2) Reorder the terms: 4(-1 + a) = 6a(3a + 2) (-1 * 4 + a * 4) = 6a(3a + 2) (-4 + 4a) = 6a(3a + 2) Reorder the terms: -4 + 4a = 6a(2 + 3a) -4 + 4a = (2 * 6a + 3a * 6a) -4 + 4a = (12a + 18a2) Solving -4 + 4a = 12a + 18a2 Solving for variable 'a'. Combine like terms: 4a + -12a = -8a -4 + -8a + -18a2 = 12a + 18a2 + -12a + -18a2 Reorder the terms: -4 + -8a + -18a2 = 12a + -12a + 18a2 + -18a2 Combine like terms: 12a + -12a = 0 -4 + -8a + -18a2 = 0 + 18a2 + -18a2 -4 + -8a + -18a2 = 18a2 + -18a2 Combine like terms: 18a2 + -18a2 = 0 -4 + -8a + -18a2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(2 + 4a + 9a2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(2 + 4a + 9a2)' equal to zero and attempt to solve: Simplifying 2 + 4a + 9a2 = 0 Solving 2 + 4a + 9a2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + 0.4444444444a + a2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 0.4444444444a + -0.2222222222 + a2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 0.4444444444a + a2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 0.4444444444a + a2 = 0 + -0.2222222222 0.4444444444a + a2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 0.4444444444a + a2 = -0.2222222222 The a term is 0.4444444444a. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444a + 0.04938271604 + a2 = -0.2222222222 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444a + a2 = -0.2222222222 + 0.04938271604 Combine like terms: -0.2222222222 + 0.04938271604 = -0.17283950616 0.04938271604 + 0.4444444444a + a2 = -0.17283950616 Factor a perfect square on the left side: (a + 0.2222222222)(a + 0.2222222222) = -0.17283950616 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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