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Simplifying 2p2 + 6p + 42 = 0 Reorder the terms: 42 + 6p + 2p2 = 0 Solving 42 + 6p + 2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 3p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 3p + p2)' equal to zero and attempt to solve: Simplifying 21 + 3p + p2 = 0 Solving 21 + 3p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 3p + -21 + p2 = 0 + -21 Reorder the terms: 21 + -21 + 3p + p2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 3p + p2 = 0 + -21 3p + p2 = 0 + -21 Combine like terms: 0 + -21 = -21 3p + p2 = -21 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 = -21 + 2.25 Reorder the terms: 2.25 + 3p + p2 = -21 + 2.25 Combine like terms: -21 + 2.25 = -18.75 2.25 + 3p + p2 = -18.75 Factor a perfect square on the left side: (p + 1.5)(p + 1.5) = -18.75 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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