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Simplifying a(2a + 3) + -2(3a + -5) = 0 Reorder the terms: a(3 + 2a) + -2(3a + -5) = 0 (3 * a + 2a * a) + -2(3a + -5) = 0 (3a + 2a2) + -2(3a + -5) = 0 Reorder the terms: 3a + 2a2 + -2(-5 + 3a) = 0 3a + 2a2 + (-5 * -2 + 3a * -2) = 0 3a + 2a2 + (10 + -6a) = 0 Reorder the terms: 10 + 3a + -6a + 2a2 = 0 Combine like terms: 3a + -6a = -3a 10 + -3a + 2a2 = 0 Solving 10 + -3a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + -1.5a + a2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -1.5a + -5 + a2 = 0 + -5 Reorder the terms: 5 + -5 + -1.5a + a2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1.5a + a2 = 0 + -5 -1.5a + a2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1.5a + a2 = -5 The a term is -1.5a. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5a + 0.5625 + a2 = -5 + 0.5625 Reorder the terms: 0.5625 + -1.5a + a2 = -5 + 0.5625 Combine like terms: -5 + 0.5625 = -4.4375 0.5625 + -1.5a + a2 = -4.4375 Factor a perfect square on the left side: (a + -0.75)(a + -0.75) = -4.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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