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Simplifying 4a + -2a(a + -3) = 16 Reorder the terms: 4a + -2a(-3 + a) = 16 4a + (-3 * -2a + a * -2a) = 16 4a + (6a + -2a2) = 16 Combine like terms: 4a + 6a = 10a 10a + -2a2 = 16 Solving 10a + -2a2 = 16 Solving for variable 'a'. Reorder the terms: -16 + 10a + -2a2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 10a + -2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 5a + -1a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 5a + -1a2)' equal to zero and attempt to solve: Simplifying -8 + 5a + -1a2 = 0 Solving -8 + 5a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -5a + a2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -5a + -8 + a2 = 0 + -8 Reorder the terms: 8 + -8 + -5a + a2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5a + a2 = 0 + -8 -5a + a2 = 0 + -8 Combine like terms: 0 + -8 = -8 -5a + a2 = -8 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = -8 + 6.25 Reorder the terms: 6.25 + -5a + a2 = -8 + 6.25 Combine like terms: -8 + 6.25 = -1.75 6.25 + -5a + a2 = -1.75 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = -1.75 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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