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Simplifying a2 + 5a = -84 Reorder the terms: 5a + a2 = -84 Solving 5a + a2 = -84 Solving for variable 'a'. Reorder the terms: 84 + 5a + a2 = -84 + 84 Combine like terms: -84 + 84 = 0 84 + 5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-84' to each side of the equation. 84 + 5a + -84 + a2 = 0 + -84 Reorder the terms: 84 + -84 + 5a + a2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + 5a + a2 = 0 + -84 5a + a2 = 0 + -84 Combine like terms: 0 + -84 = -84 5a + a2 = -84 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 = -84 + 6.25 Reorder the terms: 6.25 + 5a + a2 = -84 + 6.25 Combine like terms: -84 + 6.25 = -77.75 6.25 + 5a + a2 = -77.75 Factor a perfect square on the left side: (a + 2.5)(a + 2.5) = -77.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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