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Simplifying 8a2 + -16a = -12 Reorder the terms: -16a + 8a2 = -12 Solving -16a + 8a2 = -12 Solving for variable 'a'. Reorder the terms: 12 + -16a + 8a2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -16a + 8a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -4a + 2a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -4a + 2a2)' equal to zero and attempt to solve: Simplifying 3 + -4a + 2a2 = 0 Solving 3 + -4a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -2a + a2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2a + -1.5 + a2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2a + a2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2a + a2 = 0 + -1.5 -2a + a2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2a + a2 = -1.5 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = -1.5 + 1 Reorder the terms: 1 + -2a + a2 = -1.5 + 1 Combine like terms: -1.5 + 1 = -0.5 1 + -2a + a2 = -0.5 Factor a perfect square on the left side: (a + -1)(a + -1) = -0.5 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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