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Simplifying a2 + -3a = 2a2 + 6 + -1a + -3 + -1a + 3 Reorder the terms: -3a + a2 = 2a2 + 6 + -1a + -3 + -1a + 3 Reorder the terms: -3a + a2 = 6 + -3 + 3 + -1a + -1a + 2a2 Combine like terms: 6 + -3 = 3 -3a + a2 = 3 + 3 + -1a + -1a + 2a2 Combine like terms: 3 + 3 = 6 -3a + a2 = 6 + -1a + -1a + 2a2 Combine like terms: -1a + -1a = -2a -3a + a2 = 6 + -2a + 2a2 Solving -3a + a2 = 6 + -2a + 2a2 Solving for variable 'a'. Reorder the terms: -6 + -3a + 2a + a2 + -2a2 = 6 + -2a + 2a2 + -6 + 2a + -2a2 Combine like terms: -3a + 2a = -1a -6 + -1a + a2 + -2a2 = 6 + -2a + 2a2 + -6 + 2a + -2a2 Combine like terms: a2 + -2a2 = -1a2 -6 + -1a + -1a2 = 6 + -2a + 2a2 + -6 + 2a + -2a2 Reorder the terms: -6 + -1a + -1a2 = 6 + -6 + -2a + 2a + 2a2 + -2a2 Combine like terms: 6 + -6 = 0 -6 + -1a + -1a2 = 0 + -2a + 2a + 2a2 + -2a2 -6 + -1a + -1a2 = -2a + 2a + 2a2 + -2a2 Combine like terms: -2a + 2a = 0 -6 + -1a + -1a2 = 0 + 2a2 + -2a2 -6 + -1a + -1a2 = 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 -6 + -1a + -1a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + a + a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + a + a2)' equal to zero and attempt to solve: Simplifying 6 + a + a2 = 0 Solving 6 + a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + a + -6 + a2 = 0 + -6 Reorder the terms: 6 + -6 + a + a2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + a + a2 = 0 + -6 a + a2 = 0 + -6 Combine like terms: 0 + -6 = -6 a + a2 = -6 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. a + 0.25 + a2 = -6 + 0.25 Reorder the terms: 0.25 + a + a2 = -6 + 0.25 Combine like terms: -6 + 0.25 = -5.75 0.25 + a + a2 = -5.75 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -5.75 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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