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Simplifying 0 = p2 + 4p + 24 Reorder the terms: 0 = 24 + 4p + p2 Solving 0 = 24 + 4p + p2 Solving for variable 'p'. Combine like terms: 0 + -24 = -24 -24 + -4p + -1p2 = 24 + 4p + p2 + -24 + -4p + -1p2 Reorder the terms: -24 + -4p + -1p2 = 24 + -24 + 4p + -4p + p2 + -1p2 Combine like terms: 24 + -24 = 0 -24 + -4p + -1p2 = 0 + 4p + -4p + p2 + -1p2 -24 + -4p + -1p2 = 4p + -4p + p2 + -1p2 Combine like terms: 4p + -4p = 0 -24 + -4p + -1p2 = 0 + p2 + -1p2 -24 + -4p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -24 + -4p + -1p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 4p + p2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(24 + 4p + p2)' equal to zero and attempt to solve: Simplifying 24 + 4p + p2 = 0 Solving 24 + 4p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 4p + -24 + p2 = 0 + -24 Reorder the terms: 24 + -24 + 4p + p2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 4p + p2 = 0 + -24 4p + p2 = 0 + -24 Combine like terms: 0 + -24 = -24 4p + p2 = -24 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = -24 + 4 Reorder the terms: 4 + 4p + p2 = -24 + 4 Combine like terms: -24 + 4 = -20 4 + 4p + p2 = -20 Factor a perfect square on the left side: (p + 2)(p + 2) = -20 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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