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Simplifying -20 = 4a2 + 11a + 20 Reorder the terms: -20 = 20 + 11a + 4a2 Solving -20 = 20 + 11a + 4a2 Solving for variable 'a'. Combine like terms: -20 + -20 = -40 -40 + -11a + -4a2 = 20 + 11a + 4a2 + -20 + -11a + -4a2 Reorder the terms: -40 + -11a + -4a2 = 20 + -20 + 11a + -11a + 4a2 + -4a2 Combine like terms: 20 + -20 = 0 -40 + -11a + -4a2 = 0 + 11a + -11a + 4a2 + -4a2 -40 + -11a + -4a2 = 11a + -11a + 4a2 + -4a2 Combine like terms: 11a + -11a = 0 -40 + -11a + -4a2 = 0 + 4a2 + -4a2 -40 + -11a + -4a2 = 4a2 + -4a2 Combine like terms: 4a2 + -4a2 = 0 -40 + -11a + -4a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(40 + 11a + 4a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(40 + 11a + 4a2)' equal to zero and attempt to solve: Simplifying 40 + 11a + 4a2 = 0 Solving 40 + 11a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 10 + 2.75a + a2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 2.75a + -10 + a2 = 0 + -10 Reorder the terms: 10 + -10 + 2.75a + a2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 2.75a + a2 = 0 + -10 2.75a + a2 = 0 + -10 Combine like terms: 0 + -10 = -10 2.75a + a2 = -10 The a term is 2.75a. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75a + 1.890625 + a2 = -10 + 1.890625 Reorder the terms: 1.890625 + 2.75a + a2 = -10 + 1.890625 Combine like terms: -10 + 1.890625 = -8.109375 1.890625 + 2.75a + a2 = -8.109375 Factor a perfect square on the left side: (a + 1.375)(a + 1.375) = -8.109375 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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