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Simplifying 4 = 32 + -8a + a2 Solving 4 = 32 + -8a + a2 Solving for variable 'a'. Combine like terms: 4 + -32 = -28 -28 + 8a + -1a2 = 32 + -8a + a2 + -32 + 8a + -1a2 Reorder the terms: -28 + 8a + -1a2 = 32 + -32 + -8a + 8a + a2 + -1a2 Combine like terms: 32 + -32 = 0 -28 + 8a + -1a2 = 0 + -8a + 8a + a2 + -1a2 -28 + 8a + -1a2 = -8a + 8a + a2 + -1a2 Combine like terms: -8a + 8a = 0 -28 + 8a + -1a2 = 0 + a2 + -1a2 -28 + 8a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -28 + 8a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 28 + -8a + a2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + -8a + -28 + a2 = 0 + -28 Reorder the terms: 28 + -28 + -8a + a2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -8a + a2 = 0 + -28 -8a + a2 = 0 + -28 Combine like terms: 0 + -28 = -28 -8a + a2 = -28 The a term is -8a. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a + 16 + a2 = -28 + 16 Reorder the terms: 16 + -8a + a2 = -28 + 16 Combine like terms: -28 + 16 = -12 16 + -8a + a2 = -12 Factor a perfect square on the left side: (a + -4)(a + -4) = -12 Can't calculate square root of the right side. The solution to this equation could not be determined.
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