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Simplifying 3a2 + 2a + 21 = -7 + 3 + 2a2 Reorder the terms: 21 + 2a + 3a2 = -7 + 3 + 2a2 Combine like terms: -7 + 3 = -4 21 + 2a + 3a2 = -4 + 2a2 Solving 21 + 2a + 3a2 = -4 + 2a2 Solving for variable 'a'. Reorder the terms: 21 + 4 + 2a + 3a2 + -2a2 = -4 + 2a2 + 4 + -2a2 Combine like terms: 21 + 4 = 25 25 + 2a + 3a2 + -2a2 = -4 + 2a2 + 4 + -2a2 Combine like terms: 3a2 + -2a2 = 1a2 25 + 2a + 1a2 = -4 + 2a2 + 4 + -2a2 Reorder the terms: 25 + 2a + 1a2 = -4 + 4 + 2a2 + -2a2 Combine like terms: -4 + 4 = 0 25 + 2a + 1a2 = 0 + 2a2 + -2a2 25 + 2a + 1a2 = 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 25 + 2a + 1a2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 2a + -25 + a2 = 0 + -25 Reorder the terms: 25 + -25 + 2a + a2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 2a + a2 = 0 + -25 2a + a2 = 0 + -25 Combine like terms: 0 + -25 = -25 2a + a2 = -25 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = -25 + 1 Reorder the terms: 1 + 2a + a2 = -25 + 1 Combine like terms: -25 + 1 = -24 1 + 2a + a2 = -24 Factor a perfect square on the left side: (a + 1)(a + 1) = -24 Can't calculate square root of the right side. The solution to this equation could not be determined.
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