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Simplifying 3(p + 3)(p + 3) + 4(p + 3) + 7 = 0 Reorder the terms: 3(3 + p)(p + 3) + 4(p + 3) + 7 = 0 Reorder the terms: 3(3 + p)(3 + p) + 4(p + 3) + 7 = 0 Multiply (3 + p) * (3 + p) 3(3(3 + p) + p(3 + p)) + 4(p + 3) + 7 = 0 3((3 * 3 + p * 3) + p(3 + p)) + 4(p + 3) + 7 = 0 3((9 + 3p) + p(3 + p)) + 4(p + 3) + 7 = 0 3(9 + 3p + (3 * p + p * p)) + 4(p + 3) + 7 = 0 3(9 + 3p + (3p + p2)) + 4(p + 3) + 7 = 0 Combine like terms: 3p + 3p = 6p 3(9 + 6p + p2) + 4(p + 3) + 7 = 0 (9 * 3 + 6p * 3 + p2 * 3) + 4(p + 3) + 7 = 0 (27 + 18p + 3p2) + 4(p + 3) + 7 = 0 Reorder the terms: 27 + 18p + 3p2 + 4(3 + p) + 7 = 0 27 + 18p + 3p2 + (3 * 4 + p * 4) + 7 = 0 27 + 18p + 3p2 + (12 + 4p) + 7 = 0 Reorder the terms: 27 + 12 + 7 + 18p + 4p + 3p2 = 0 Combine like terms: 27 + 12 = 39 39 + 7 + 18p + 4p + 3p2 = 0 Combine like terms: 39 + 7 = 46 46 + 18p + 4p + 3p2 = 0 Combine like terms: 18p + 4p = 22p 46 + 22p + 3p2 = 0 Solving 46 + 22p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 15.33333333 + 7.333333333p + p2 = 0 Move the constant term to the right: Add '-15.33333333' to each side of the equation. 15.33333333 + 7.333333333p + -15.33333333 + p2 = 0 + -15.33333333 Reorder the terms: 15.33333333 + -15.33333333 + 7.333333333p + p2 = 0 + -15.33333333 Combine like terms: 15.33333333 + -15.33333333 = 0.00000000 0.00000000 + 7.333333333p + p2 = 0 + -15.33333333 7.333333333p + p2 = 0 + -15.33333333 Combine like terms: 0 + -15.33333333 = -15.33333333 7.333333333p + p2 = -15.33333333 The p term is 7.333333333p. Take half its coefficient (3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. 7.333333333p + 13.44444445 + p2 = -15.33333333 + 13.44444445 Reorder the terms: 13.44444445 + 7.333333333p + p2 = -15.33333333 + 13.44444445 Combine like terms: -15.33333333 + 13.44444445 = -1.88888888 13.44444445 + 7.333333333p + p2 = -1.88888888 Factor a perfect square on the left side: (p + 3.666666667)(p + 3.666666667) = -1.88888888 Can't calculate square root of the right side. The solution to this equation could not be determined.
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