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Simplifying (9a2 + a + -5) + -1(4a2 + 9a + -9) = 0 Reorder the terms: (-5 + a + 9a2) + -1(4a2 + 9a + -9) = 0 Remove parenthesis around (-5 + a + 9a2) -5 + a + 9a2 + -1(4a2 + 9a + -9) = 0 Reorder the terms: -5 + a + 9a2 + -1(-9 + 9a + 4a2) = 0 -5 + a + 9a2 + (-9 * -1 + 9a * -1 + 4a2 * -1) = 0 -5 + a + 9a2 + (9 + -9a + -4a2) = 0 Reorder the terms: -5 + 9 + a + -9a + 9a2 + -4a2 = 0 Combine like terms: -5 + 9 = 4 4 + a + -9a + 9a2 + -4a2 = 0 Combine like terms: a + -9a = -8a 4 + -8a + 9a2 + -4a2 = 0 Combine like terms: 9a2 + -4a2 = 5a2 4 + -8a + 5a2 = 0 Solving 4 + -8a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -1.6a + a2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -1.6a + -0.8 + a2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -1.6a + a2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -1.6a + a2 = 0 + -0.8 -1.6a + a2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -1.6a + a2 = -0.8 The a term is -1.6a. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6a + 0.64 + a2 = -0.8 + 0.64 Reorder the terms: 0.64 + -1.6a + a2 = -0.8 + 0.64 Combine like terms: -0.8 + 0.64 = -0.16 0.64 + -1.6a + a2 = -0.16 Factor a perfect square on the left side: (a + -0.8)(a + -0.8) = -0.16 Can't calculate square root of the right side. The solution to this equation could not be determined.
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