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Simplifying -6a2 + 3a + 7 + 8a2 + -7a + 5 = 0 Reorder the terms: 7 + 5 + 3a + -7a + -6a2 + 8a2 = 0 Combine like terms: 7 + 5 = 12 12 + 3a + -7a + -6a2 + 8a2 = 0 Combine like terms: 3a + -7a = -4a 12 + -4a + -6a2 + 8a2 = 0 Combine like terms: -6a2 + 8a2 = 2a2 12 + -4a + 2a2 = 0 Solving 12 + -4a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -2a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -2a + a2)' equal to zero and attempt to solve: Simplifying 6 + -2a + a2 = 0 Solving 6 + -2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -2a + -6 + a2 = 0 + -6 Reorder the terms: 6 + -6 + -2a + a2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -2a + a2 = 0 + -6 -2a + a2 = 0 + -6 Combine like terms: 0 + -6 = -6 -2a + a2 = -6 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 = -6 + 1 Reorder the terms: 1 + -2a + a2 = -6 + 1 Combine like terms: -6 + 1 = -5 1 + -2a + a2 = -5 Factor a perfect square on the left side: (a + -1)(a + -1) = -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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