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Simplifying 4Q2 + 4Q + 32 = 0 Reorder the terms: 32 + 4Q + 4Q2 = 0 Solving 32 + 4Q + 4Q2 = 0 Solving for variable 'Q'. Factor out the Greatest Common Factor (GCF), '4'. 4(8 + Q + Q2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + Q + Q2)' equal to zero and attempt to solve: Simplifying 8 + Q + Q2 = 0 Solving 8 + Q + Q2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + Q + -8 + Q2 = 0 + -8 Reorder the terms: 8 + -8 + Q + Q2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + Q + Q2 = 0 + -8 Q + Q2 = 0 + -8 Combine like terms: 0 + -8 = -8 Q + Q2 = -8 The Q term is Q. 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. Q + 0.25 + Q2 = -8 + 0.25 Reorder the terms: 0.25 + Q + Q2 = -8 + 0.25 Combine like terms: -8 + 0.25 = -7.75 0.25 + Q + Q2 = -7.75 Factor a perfect square on the left side: (Q + 0.5)(Q + 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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