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Simplifying a = 4a2 + -2a + 10 Reorder the terms: a = 10 + -2a + 4a2 Solving a = 10 + -2a + 4a2 Solving for variable 'a'. Reorder the terms: -10 + a + 2a + -4a2 = 10 + -2a + 4a2 + -10 + 2a + -4a2 Combine like terms: a + 2a = 3a -10 + 3a + -4a2 = 10 + -2a + 4a2 + -10 + 2a + -4a2 Reorder the terms: -10 + 3a + -4a2 = 10 + -10 + -2a + 2a + 4a2 + -4a2 Combine like terms: 10 + -10 = 0 -10 + 3a + -4a2 = 0 + -2a + 2a + 4a2 + -4a2 -10 + 3a + -4a2 = -2a + 2a + 4a2 + -4a2 Combine like terms: -2a + 2a = 0 -10 + 3a + -4a2 = 0 + 4a2 + -4a2 -10 + 3a + -4a2 = 4a2 + -4a2 Combine like terms: 4a2 + -4a2 = 0 -10 + 3a + -4a2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 2.5 + -0.75a + a2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -0.75a + -2.5 + a2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -0.75a + a2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -0.75a + a2 = 0 + -2.5 -0.75a + a2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -0.75a + a2 = -2.5 The a term is -0.75a. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75a + 0.140625 + a2 = -2.5 + 0.140625 Reorder the terms: 0.140625 + -0.75a + a2 = -2.5 + 0.140625 Combine like terms: -2.5 + 0.140625 = -2.359375 0.140625 + -0.75a + a2 = -2.359375 Factor a perfect square on the left side: (a + -0.375)(a + -0.375) = -2.359375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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