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Simplifying 5 + -2(4a + 1) * 3a = 13 Reorder the terms: 5 + -2(1 + 4a) * 3a = 13 Reorder the terms for easier multiplication: 5 + -2 * 3a(1 + 4a) = 13 Multiply -2 * 3 5 + -6a(1 + 4a) = 13 5 + (1 * -6a + 4a * -6a) = 13 5 + (-6a + -24a2) = 13 Solving 5 + -6a + -24a2 = 13 Solving for variable 'a'. Reorder the terms: 5 + -13 + -6a + -24a2 = 13 + -13 Combine like terms: 5 + -13 = -8 -8 + -6a + -24a2 = 13 + -13 Combine like terms: 13 + -13 = 0 -8 + -6a + -24a2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + 3a + 12a2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + 3a + 12a2)' equal to zero and attempt to solve: Simplifying 4 + 3a + 12a2 = 0 Solving 4 + 3a + 12a2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.3333333333 + 0.25a + a2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.25a + -0.3333333333 + a2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.25a + a2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.25a + a2 = 0 + -0.3333333333 0.25a + a2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.25a + a2 = -0.3333333333 The a term is 0.25a. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25a + 0.015625 + a2 = -0.3333333333 + 0.015625 Reorder the terms: 0.015625 + 0.25a + a2 = -0.3333333333 + 0.015625 Combine like terms: -0.3333333333 + 0.015625 = -0.3177083333 0.015625 + 0.25a + a2 = -0.3177083333 Factor a perfect square on the left side: (a + 0.125)(a + 0.125) = -0.3177083333 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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