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Simplifying (2p + 5)(-4) = p2 + 20 Reorder the terms: (5 + 2p)(-4) = p2 + 20 Reorder the terms for easier multiplication: -4(5 + 2p) = p2 + 20 (5 * -4 + 2p * -4) = p2 + 20 (-20 + -8p) = p2 + 20 Reorder the terms: -20 + -8p = 20 + p2 Solving -20 + -8p = 20 + p2 Solving for variable 'p'. Reorder the terms: -20 + -20 + -8p + -1p2 = 20 + p2 + -20 + -1p2 Combine like terms: -20 + -20 = -40 -40 + -8p + -1p2 = 20 + p2 + -20 + -1p2 Reorder the terms: -40 + -8p + -1p2 = 20 + -20 + p2 + -1p2 Combine like terms: 20 + -20 = 0 -40 + -8p + -1p2 = 0 + p2 + -1p2 -40 + -8p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -40 + -8p + -1p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(40 + 8p + p2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(40 + 8p + p2)' equal to zero and attempt to solve: Simplifying 40 + 8p + p2 = 0 Solving 40 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 8p + -40 + p2 = 0 + -40 Reorder the terms: 40 + -40 + 8p + p2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 8p + p2 = 0 + -40 8p + p2 = 0 + -40 Combine like terms: 0 + -40 = -40 8p + p2 = -40 The p term is 8p. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8p + 16 + p2 = -40 + 16 Reorder the terms: 16 + 8p + p2 = -40 + 16 Combine like terms: -40 + 16 = -24 16 + 8p + p2 = -24 Factor a perfect square on the left side: (p + 4)(p + 4) = -24 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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