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Simplifying a(7 + 7a) = 8a + -32 (7 * a + 7a * a) = 8a + -32 (7a + 7a2) = 8a + -32 Reorder the terms: 7a + 7a2 = -32 + 8a Solving 7a + 7a2 = -32 + 8a Solving for variable 'a'. Reorder the terms: 32 + 7a + -8a + 7a2 = -32 + 8a + 32 + -8a Combine like terms: 7a + -8a = -1a 32 + -1a + 7a2 = -32 + 8a + 32 + -8a Reorder the terms: 32 + -1a + 7a2 = -32 + 32 + 8a + -8a Combine like terms: -32 + 32 = 0 32 + -1a + 7a2 = 0 + 8a + -8a 32 + -1a + 7a2 = 8a + -8a Combine like terms: 8a + -8a = 0 32 + -1a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 4.571428571 + -0.1428571429a + a2 = 0 Move the constant term to the right: Add '-4.571428571' to each side of the equation. 4.571428571 + -0.1428571429a + -4.571428571 + a2 = 0 + -4.571428571 Reorder the terms: 4.571428571 + -4.571428571 + -0.1428571429a + a2 = 0 + -4.571428571 Combine like terms: 4.571428571 + -4.571428571 = 0.000000000 0.000000000 + -0.1428571429a + a2 = 0 + -4.571428571 -0.1428571429a + a2 = 0 + -4.571428571 Combine like terms: 0 + -4.571428571 = -4.571428571 -0.1428571429a + a2 = -4.571428571 The a term is -0.1428571429a. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429a + 0.005102040819 + a2 = -4.571428571 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429a + a2 = -4.571428571 + 0.005102040819 Combine like terms: -4.571428571 + 0.005102040819 = -4.566326530181 0.005102040819 + -0.1428571429a + a2 = -4.566326530181 Factor a perfect square on the left side: (a + -0.07142857145)(a + -0.07142857145) = -4.566326530181 Can't calculate square root of the right side. The solution to this equation could not be determined.
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