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Simplifying a(a + -2) = 3(a + -5) Reorder the terms: a(-2 + a) = 3(a + -5) (-2 * a + a * a) = 3(a + -5) (-2a + a2) = 3(a + -5) Reorder the terms: -2a + a2 = 3(-5 + a) -2a + a2 = (-5 * 3 + a * 3) -2a + a2 = (-15 + 3a) Solving -2a + a2 = -15 + 3a Solving for variable 'a'. Reorder the terms: 15 + -2a + -3a + a2 = -15 + 3a + 15 + -3a Combine like terms: -2a + -3a = -5a 15 + -5a + a2 = -15 + 3a + 15 + -3a Reorder the terms: 15 + -5a + a2 = -15 + 15 + 3a + -3a Combine like terms: -15 + 15 = 0 15 + -5a + a2 = 0 + 3a + -3a 15 + -5a + a2 = 3a + -3a Combine like terms: 3a + -3a = 0 15 + -5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -5a + -15 + a2 = 0 + -15 Reorder the terms: 15 + -15 + -5a + a2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -5a + a2 = 0 + -15 -5a + a2 = 0 + -15 Combine like terms: 0 + -15 = -15 -5a + a2 = -15 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = -15 + 6.25 Reorder the terms: 6.25 + -5a + a2 = -15 + 6.25 Combine like terms: -15 + 6.25 = -8.75 6.25 + -5a + a2 = -8.75 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = -8.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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