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Simplifying -0.1p + -0.03p(5 + -6p) = 0.06(p + -5) + -0.09 -0.1p + (5 * -0.03p + -6p * -0.03p) = 0.06(p + -5) + -0.09 -0.1p + (-0.15p + 0.18p2) = 0.06(p + -5) + -0.09 Combine like terms: -0.1p + -0.15p = -0.25p -0.25p + 0.18p2 = 0.06(p + -5) + -0.09 Reorder the terms: -0.25p + 0.18p2 = 0.06(-5 + p) + -0.09 -0.25p + 0.18p2 = (-5 * 0.06 + p * 0.06) + -0.09 -0.25p + 0.18p2 = (-0.3 + 0.06p) + -0.09 Reorder the terms: -0.25p + 0.18p2 = -0.3 + -0.09 + 0.06p Combine like terms: -0.3 + -0.09 = -0.39 -0.25p + 0.18p2 = -0.39 + 0.06p Solving -0.25p + 0.18p2 = -0.39 + 0.06p Solving for variable 'p'. Reorder the terms: 0.39 + -0.25p + -0.06p + 0.18p2 = -0.39 + 0.06p + 0.39 + -0.06p Combine like terms: -0.25p + -0.06p = -0.31p 0.39 + -0.31p + 0.18p2 = -0.39 + 0.06p + 0.39 + -0.06p Reorder the terms: 0.39 + -0.31p + 0.18p2 = -0.39 + 0.39 + 0.06p + -0.06p Combine like terms: -0.39 + 0.39 = 0.00 0.39 + -0.31p + 0.18p2 = 0.00 + 0.06p + -0.06p 0.39 + -0.31p + 0.18p2 = 0.06p + -0.06p Combine like terms: 0.06p + -0.06p = 0.00 0.39 + -0.31p + 0.18p2 = 0.00 Begin completing the square. Divide all terms by 0.18 the coefficient of the squared term: Divide each side by '0.18'. 2.166666667 + -1.722222222p + p2 = 0 Move the constant term to the right: Add '-2.166666667' to each side of the equation. 2.166666667 + -1.722222222p + -2.166666667 + p2 = 0 + -2.166666667 Reorder the terms: 2.166666667 + -2.166666667 + -1.722222222p + p2 = 0 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + -1.722222222p + p2 = 0 + -2.166666667 -1.722222222p + p2 = 0 + -2.166666667 Combine like terms: 0 + -2.166666667 = -2.166666667 -1.722222222p + p2 = -2.166666667 The p term is -1.722222222p. Take half its coefficient (-0.861111111). Square it (0.7415123455) and add it to both sides. Add '0.7415123455' to each side of the equation. -1.722222222p + 0.7415123455 + p2 = -2.166666667 + 0.7415123455 Reorder the terms: 0.7415123455 + -1.722222222p + p2 = -2.166666667 + 0.7415123455 Combine like terms: -2.166666667 + 0.7415123455 = -1.4251543215 0.7415123455 + -1.722222222p + p2 = -1.4251543215 Factor a perfect square on the left side: (p + -0.861111111)(p + -0.861111111) = -1.4251543215 Can't calculate square root of the right side. The solution to this equation could not be determined.
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