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Simplifying 6p2 + 54p + 180 = 0 Reorder the terms: 180 + 54p + 6p2 = 0 Solving 180 + 54p + 6p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '6'. 6(30 + 9p + p2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(30 + 9p + p2)' equal to zero and attempt to solve: Simplifying 30 + 9p + p2 = 0 Solving 30 + 9p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 9p + -30 + p2 = 0 + -30 Reorder the terms: 30 + -30 + 9p + p2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 9p + p2 = 0 + -30 9p + p2 = 0 + -30 Combine like terms: 0 + -30 = -30 9p + p2 = -30 The p term is 9p. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9p + 20.25 + p2 = -30 + 20.25 Reorder the terms: 20.25 + 9p + p2 = -30 + 20.25 Combine like terms: -30 + 20.25 = -9.75 20.25 + 9p + p2 = -9.75 Factor a perfect square on the left side: (p + 4.5)(p + 4.5) = -9.75 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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