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Simplifying 5a2 = -8 + a Solving 5a2 = -8 + a Solving for variable 'a'. Reorder the terms: 8 + -1a + 5a2 = -8 + a + 8 + -1a Reorder the terms: 8 + -1a + 5a2 = -8 + 8 + a + -1a Combine like terms: -8 + 8 = 0 8 + -1a + 5a2 = 0 + a + -1a 8 + -1a + 5a2 = a + -1a Combine like terms: a + -1a = 0 8 + -1a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + -0.2a + a2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -0.2a + -1.6 + a2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -0.2a + a2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -0.2a + a2 = 0 + -1.6 -0.2a + a2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -0.2a + a2 = -1.6 The a term is -0.2a. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2a + 0.01 + a2 = -1.6 + 0.01 Reorder the terms: 0.01 + -0.2a + a2 = -1.6 + 0.01 Combine like terms: -1.6 + 0.01 = -1.59 0.01 + -0.2a + a2 = -1.59 Factor a perfect square on the left side: (a + -0.1)(a + -0.1) = -1.59 Can't calculate square root of the right side. The solution to this equation could not be determined.
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