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Simplifying (-1a2 + 1) + -1(a2 + -2) + (6a2 + -7a + 4) = 0 Reorder the terms: (1 + -1a2) + -1(a2 + -2) + (6a2 + -7a + 4) = 0 Remove parenthesis around (1 + -1a2) 1 + -1a2 + -1(a2 + -2) + (6a2 + -7a + 4) = 0 Reorder the terms: 1 + -1a2 + -1(-2 + a2) + (6a2 + -7a + 4) = 0 1 + -1a2 + (-2 * -1 + a2 * -1) + (6a2 + -7a + 4) = 0 1 + -1a2 + (2 + -1a2) + (6a2 + -7a + 4) = 0 Reorder the terms: 1 + -1a2 + 2 + -1a2 + (4 + -7a + 6a2) = 0 Remove parenthesis around (4 + -7a + 6a2) 1 + -1a2 + 2 + -1a2 + 4 + -7a + 6a2 = 0 Reorder the terms: 1 + 2 + 4 + -7a + -1a2 + -1a2 + 6a2 = 0 Combine like terms: 1 + 2 = 3 3 + 4 + -7a + -1a2 + -1a2 + 6a2 = 0 Combine like terms: 3 + 4 = 7 7 + -7a + -1a2 + -1a2 + 6a2 = 0 Combine like terms: -1a2 + -1a2 = -2a2 7 + -7a + -2a2 + 6a2 = 0 Combine like terms: -2a2 + 6a2 = 4a2 7 + -7a + 4a2 = 0 Solving 7 + -7a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -1.75a + a2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -1.75a + -1.75 + a2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -1.75a + a2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -1.75a + a2 = 0 + -1.75 -1.75a + a2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -1.75a + a2 = -1.75 The a term is -1.75a. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75a + 0.765625 + a2 = -1.75 + 0.765625 Reorder the terms: 0.765625 + -1.75a + a2 = -1.75 + 0.765625 Combine like terms: -1.75 + 0.765625 = -0.984375 0.765625 + -1.75a + a2 = -0.984375 Factor a perfect square on the left side: (a + -0.875)(a + -0.875) = -0.984375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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