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Simplifying -142 = 2(8a + 1) * 2a Reorder the terms: -142 = 2(1 + 8a) * 2a Reorder the terms for easier multiplication: -142 = 2 * 2a(1 + 8a) Multiply 2 * 2 -142 = 4a(1 + 8a) -142 = (1 * 4a + 8a * 4a) -142 = (4a + 32a2) Solving -142 = 4a + 32a2 Solving for variable 'a'. Reorder the terms: -142 + -4a + -32a2 = 4a + -4a + 32a2 + -32a2 Combine like terms: 4a + -4a = 0 -142 + -4a + -32a2 = 0 + 32a2 + -32a2 -142 + -4a + -32a2 = 32a2 + -32a2 Combine like terms: 32a2 + -32a2 = 0 -142 + -4a + -32a2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(71 + 2a + 16a2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(71 + 2a + 16a2)' equal to zero and attempt to solve: Simplifying 71 + 2a + 16a2 = 0 Solving 71 + 2a + 16a2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 4.4375 + 0.125a + a2 = 0 Move the constant term to the right: Add '-4.4375' to each side of the equation. 4.4375 + 0.125a + -4.4375 + a2 = 0 + -4.4375 Reorder the terms: 4.4375 + -4.4375 + 0.125a + a2 = 0 + -4.4375 Combine like terms: 4.4375 + -4.4375 = 0.0000 0.0000 + 0.125a + a2 = 0 + -4.4375 0.125a + a2 = 0 + -4.4375 Combine like terms: 0 + -4.4375 = -4.4375 0.125a + a2 = -4.4375 The a term is 0.125a. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125a + 0.00390625 + a2 = -4.4375 + 0.00390625 Reorder the terms: 0.00390625 + 0.125a + a2 = -4.4375 + 0.00390625 Combine like terms: -4.4375 + 0.00390625 = -4.43359375 0.00390625 + 0.125a + a2 = -4.43359375 Factor a perfect square on the left side: (a + 0.0625)(a + 0.0625) = -4.43359375 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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