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Simplifying 3a2 + 33a + 100 = 0 Reorder the terms: 100 + 33a + 3a2 = 0 Solving 100 + 33a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 33.33333333 + 11a + a2 = 0 Move the constant term to the right: Add '-33.33333333' to each side of the equation. 33.33333333 + 11a + -33.33333333 + a2 = 0 + -33.33333333 Reorder the terms: 33.33333333 + -33.33333333 + 11a + a2 = 0 + -33.33333333 Combine like terms: 33.33333333 + -33.33333333 = 0.00000000 0.00000000 + 11a + a2 = 0 + -33.33333333 11a + a2 = 0 + -33.33333333 Combine like terms: 0 + -33.33333333 = -33.33333333 11a + a2 = -33.33333333 The a term is 11a. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11a + 30.25 + a2 = -33.33333333 + 30.25 Reorder the terms: 30.25 + 11a + a2 = -33.33333333 + 30.25 Combine like terms: -33.33333333 + 30.25 = -3.08333333 30.25 + 11a + a2 = -3.08333333 Factor a perfect square on the left side: (a + 5.5)(a + 5.5) = -3.08333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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