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Simplifying 7a + -16 = -2a(-5a + 2) + 3 Reorder the terms: -16 + 7a = -2a(-5a + 2) + 3 Reorder the terms: -16 + 7a = -2a(2 + -5a) + 3 -16 + 7a = (2 * -2a + -5a * -2a) + 3 -16 + 7a = (-4a + 10a2) + 3 Reorder the terms: -16 + 7a = 3 + -4a + 10a2 Solving -16 + 7a = 3 + -4a + 10a2 Solving for variable 'a'. Reorder the terms: -16 + -3 + 7a + 4a + -10a2 = 3 + -4a + 10a2 + -3 + 4a + -10a2 Combine like terms: -16 + -3 = -19 -19 + 7a + 4a + -10a2 = 3 + -4a + 10a2 + -3 + 4a + -10a2 Combine like terms: 7a + 4a = 11a -19 + 11a + -10a2 = 3 + -4a + 10a2 + -3 + 4a + -10a2 Reorder the terms: -19 + 11a + -10a2 = 3 + -3 + -4a + 4a + 10a2 + -10a2 Combine like terms: 3 + -3 = 0 -19 + 11a + -10a2 = 0 + -4a + 4a + 10a2 + -10a2 -19 + 11a + -10a2 = -4a + 4a + 10a2 + -10a2 Combine like terms: -4a + 4a = 0 -19 + 11a + -10a2 = 0 + 10a2 + -10a2 -19 + 11a + -10a2 = 10a2 + -10a2 Combine like terms: 10a2 + -10a2 = 0 -19 + 11a + -10a2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 1.9 + -1.1a + a2 = 0 Move the constant term to the right: Add '-1.9' to each side of the equation. 1.9 + -1.1a + -1.9 + a2 = 0 + -1.9 Reorder the terms: 1.9 + -1.9 + -1.1a + a2 = 0 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + -1.1a + a2 = 0 + -1.9 -1.1a + a2 = 0 + -1.9 Combine like terms: 0 + -1.9 = -1.9 -1.1a + a2 = -1.9 The a term is -1.1a. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1a + 0.3025 + a2 = -1.9 + 0.3025 Reorder the terms: 0.3025 + -1.1a + a2 = -1.9 + 0.3025 Combine like terms: -1.9 + 0.3025 = -1.5975 0.3025 + -1.1a + a2 = -1.5975 Factor a perfect square on the left side: (a + -0.55)(a + -0.55) = -1.5975 Can't calculate square root of the right side. The solution to this equation could not be determined.
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