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Simplifying 12a + -6a2 = 48 Solving 12a + -6a2 = 48 Solving for variable 'a'. Reorder the terms: -48 + 12a + -6a2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 12a + -6a2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-8 + 2a + -1a2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-8 + 2a + -1a2)' equal to zero and attempt to solve: Simplifying -8 + 2a + -1a2 = 0 Solving -8 + 2a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -2a + a2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -2a + -8 + a2 = 0 + -8 Reorder the terms: 8 + -8 + -2a + a2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -2a + a2 = 0 + -8 -2a + a2 = 0 + -8 Combine like terms: 0 + -8 = -8 -2a + a2 = -8 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 = -8 + 1 Reorder the terms: 1 + -2a + a2 = -8 + 1 Combine like terms: -8 + 1 = -7 1 + -2a + a2 = -7 Factor a perfect square on the left side: (a + -1)(a + -1) = -7 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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