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Simplifying 3p2 + 9p + 42 = 0 Reorder the terms: 42 + 9p + 3p2 = 0 Solving 42 + 9p + 3p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + 3p + p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(14 + 3p + p2)' equal to zero and attempt to solve: Simplifying 14 + 3p + p2 = 0 Solving 14 + 3p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 3p + -14 + p2 = 0 + -14 Reorder the terms: 14 + -14 + 3p + p2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 3p + p2 = 0 + -14 3p + p2 = 0 + -14 Combine like terms: 0 + -14 = -14 3p + p2 = -14 The p term is 3p. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3p + 2.25 + p2 = -14 + 2.25 Reorder the terms: 2.25 + 3p + p2 = -14 + 2.25 Combine like terms: -14 + 2.25 = -11.75 2.25 + 3p + p2 = -11.75 Factor a perfect square on the left side: (p + 1.5)(p + 1.5) = -11.75 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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