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Simplifying 8(7 + -1p) + -8 = -16p(p + -2) (7 * 8 + -1p * 8) + -8 = -16p(p + -2) (56 + -8p) + -8 = -16p(p + -2) Reorder the terms: 56 + -8 + -8p = -16p(p + -2) Combine like terms: 56 + -8 = 48 48 + -8p = -16p(p + -2) Reorder the terms: 48 + -8p = -16p(-2 + p) 48 + -8p = (-2 * -16p + p * -16p) 48 + -8p = (32p + -16p2) Solving 48 + -8p = 32p + -16p2 Solving for variable 'p'. Combine like terms: -8p + -32p = -40p 48 + -40p + 16p2 = 32p + -16p2 + -32p + 16p2 Reorder the terms: 48 + -40p + 16p2 = 32p + -32p + -16p2 + 16p2 Combine like terms: 32p + -32p = 0 48 + -40p + 16p2 = 0 + -16p2 + 16p2 48 + -40p + 16p2 = -16p2 + 16p2 Combine like terms: -16p2 + 16p2 = 0 48 + -40p + 16p2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(6 + -5p + 2p2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(6 + -5p + 2p2)' equal to zero and attempt to solve: Simplifying 6 + -5p + 2p2 = 0 Solving 6 + -5p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + -2.5p + p2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2.5p + -3 + p2 = 0 + -3 Reorder the terms: 3 + -3 + -2.5p + p2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2.5p + p2 = 0 + -3 -2.5p + p2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2.5p + p2 = -3 The p term is -2.5p. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5p + 1.5625 + p2 = -3 + 1.5625 Reorder the terms: 1.5625 + -2.5p + p2 = -3 + 1.5625 Combine like terms: -3 + 1.5625 = -1.4375 1.5625 + -2.5p + p2 = -1.4375 Factor a perfect square on the left side: (p + -1.25)(p + -1.25) = -1.4375 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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