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Simplifying 4a + (16a2 + -8a + 24) = 0 Reorder the terms: 4a + (24 + -8a + 16a2) = 0 Remove parenthesis around (24 + -8a + 16a2) 4a + 24 + -8a + 16a2 = 0 Reorder the terms: 24 + 4a + -8a + 16a2 = 0 Combine like terms: 4a + -8a = -4a 24 + -4a + 16a2 = 0 Solving 24 + -4a + 16a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + -1a + 4a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + -1a + 4a2)' equal to zero and attempt to solve: Simplifying 6 + -1a + 4a2 = 0 Solving 6 + -1a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.5 + -0.25a + a2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.25a + -1.5 + a2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.25a + a2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.25a + a2 = 0 + -1.5 -0.25a + a2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.25a + a2 = -1.5 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 = -1.5 + 0.015625 Reorder the terms: 0.015625 + -0.25a + a2 = -1.5 + 0.015625 Combine like terms: -1.5 + 0.015625 = -1.484375 0.015625 + -0.25a + a2 = -1.484375 Factor a perfect square on the left side: (a + -0.125)(a + -0.125) = -1.484375 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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