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Simplifying 4a2 + -4a = -32 Reorder the terms: -4a + 4a2 = -32 Solving -4a + 4a2 = -32 Solving for variable 'a'. Reorder the terms: 32 + -4a + 4a2 = -32 + 32 Combine like terms: -32 + 32 = 0 32 + -4a + 4a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(8 + -1a + a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + -1a + a2)' equal to zero and attempt to solve: Simplifying 8 + -1a + a2 = 0 Solving 8 + -1a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -1a + -8 + a2 = 0 + -8 Reorder the terms: 8 + -8 + -1a + a2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1a + a2 = 0 + -8 -1a + a2 = 0 + -8 Combine like terms: 0 + -8 = -8 -1a + a2 = -8 The a term is -1a. 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. -1a + 0.25 + a2 = -8 + 0.25 Reorder the terms: 0.25 + -1a + a2 = -8 + 0.25 Combine like terms: -8 + 0.25 = -7.75 0.25 + -1a + a2 = -7.75 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = -7.75 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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