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Simplifying 3a2 + 6a + 78 = 0 Reorder the terms: 78 + 6a + 3a2 = 0 Solving 78 + 6a + 3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(26 + 2a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(26 + 2a + a2)' equal to zero and attempt to solve: Simplifying 26 + 2a + a2 = 0 Solving 26 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + 2a + -26 + a2 = 0 + -26 Reorder the terms: 26 + -26 + 2a + a2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 2a + a2 = 0 + -26 2a + a2 = 0 + -26 Combine like terms: 0 + -26 = -26 2a + a2 = -26 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 = -26 + 1 Reorder the terms: 1 + 2a + a2 = -26 + 1 Combine like terms: -26 + 1 = -25 1 + 2a + a2 = -25 Factor a perfect square on the left side: (a + 1)(a + 1) = -25 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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