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Simplifying 8(7 + -1p) + -8 = -18p(p + -2) (7 * 8 + -1p * 8) + -8 = -18p(p + -2) (56 + -8p) + -8 = -18p(p + -2) Reorder the terms: 56 + -8 + -8p = -18p(p + -2) Combine like terms: 56 + -8 = 48 48 + -8p = -18p(p + -2) Reorder the terms: 48 + -8p = -18p(-2 + p) 48 + -8p = (-2 * -18p + p * -18p) 48 + -8p = (36p + -18p2) Solving 48 + -8p = 36p + -18p2 Solving for variable 'p'. Combine like terms: -8p + -36p = -44p 48 + -44p + 18p2 = 36p + -18p2 + -36p + 18p2 Reorder the terms: 48 + -44p + 18p2 = 36p + -36p + -18p2 + 18p2 Combine like terms: 36p + -36p = 0 48 + -44p + 18p2 = 0 + -18p2 + 18p2 48 + -44p + 18p2 = -18p2 + 18p2 Combine like terms: -18p2 + 18p2 = 0 48 + -44p + 18p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -22p + 9p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -22p + 9p2)' equal to zero and attempt to solve: Simplifying 24 + -22p + 9p2 = 0 Solving 24 + -22p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.666666667 + -2.444444444p + p2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -2.444444444p + -2.666666667 + p2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -2.444444444p + p2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -2.444444444p + p2 = 0 + -2.666666667 -2.444444444p + p2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -2.444444444p + p2 = -2.666666667 The p term is -2.444444444p. Take half its coefficient (-1.222222222). Square it (1.493827160) and add it to both sides. Add '1.493827160' to each side of the equation. -2.444444444p + 1.493827160 + p2 = -2.666666667 + 1.493827160 Reorder the terms: 1.493827160 + -2.444444444p + p2 = -2.666666667 + 1.493827160 Combine like terms: -2.666666667 + 1.493827160 = -1.172839507 1.493827160 + -2.444444444p + p2 = -1.172839507 Factor a perfect square on the left side: (p + -1.222222222)(p + -1.222222222) = -1.172839507 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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