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Simplifying 2a2 + 16a = -42 Reorder the terms: 16a + 2a2 = -42 Solving 16a + 2a2 = -42 Solving for variable 'a'. Reorder the terms: 42 + 16a + 2a2 = -42 + 42 Combine like terms: -42 + 42 = 0 42 + 16a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 8a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 8a + a2)' equal to zero and attempt to solve: Simplifying 21 + 8a + a2 = 0 Solving 21 + 8a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 8a + -21 + a2 = 0 + -21 Reorder the terms: 21 + -21 + 8a + a2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 8a + a2 = 0 + -21 8a + a2 = 0 + -21 Combine like terms: 0 + -21 = -21 8a + a2 = -21 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 = -21 + 16 Reorder the terms: 16 + 8a + a2 = -21 + 16 Combine like terms: -21 + 16 = -5 16 + 8a + a2 = -5 Factor a perfect square on the left side: (a + 4)(a + 4) = -5 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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