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Simplifying p + 4 = 3p2 + 5p + 72 Reorder the terms: 4 + p = 3p2 + 5p + 72 Reorder the terms: 4 + p = 72 + 5p + 3p2 Solving 4 + p = 72 + 5p + 3p2 Solving for variable 'p'. Reorder the terms: 4 + -72 + p + -5p + -3p2 = 72 + 5p + 3p2 + -72 + -5p + -3p2 Combine like terms: 4 + -72 = -68 -68 + p + -5p + -3p2 = 72 + 5p + 3p2 + -72 + -5p + -3p2 Combine like terms: p + -5p = -4p -68 + -4p + -3p2 = 72 + 5p + 3p2 + -72 + -5p + -3p2 Reorder the terms: -68 + -4p + -3p2 = 72 + -72 + 5p + -5p + 3p2 + -3p2 Combine like terms: 72 + -72 = 0 -68 + -4p + -3p2 = 0 + 5p + -5p + 3p2 + -3p2 -68 + -4p + -3p2 = 5p + -5p + 3p2 + -3p2 Combine like terms: 5p + -5p = 0 -68 + -4p + -3p2 = 0 + 3p2 + -3p2 -68 + -4p + -3p2 = 3p2 + -3p2 Combine like terms: 3p2 + -3p2 = 0 -68 + -4p + -3p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(68 + 4p + 3p2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(68 + 4p + 3p2)' equal to zero and attempt to solve: Simplifying 68 + 4p + 3p2 = 0 Solving 68 + 4p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 22.66666667 + 1.333333333p + p2 = 0 Move the constant term to the right: Add '-22.66666667' to each side of the equation. 22.66666667 + 1.333333333p + -22.66666667 + p2 = 0 + -22.66666667 Reorder the terms: 22.66666667 + -22.66666667 + 1.333333333p + p2 = 0 + -22.66666667 Combine like terms: 22.66666667 + -22.66666667 = 0.00000000 0.00000000 + 1.333333333p + p2 = 0 + -22.66666667 1.333333333p + p2 = 0 + -22.66666667 Combine like terms: 0 + -22.66666667 = -22.66666667 1.333333333p + p2 = -22.66666667 The p term is 1.333333333p. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333p + 0.4444444442 + p2 = -22.66666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333p + p2 = -22.66666667 + 0.4444444442 Combine like terms: -22.66666667 + 0.4444444442 = -22.2222222258 0.4444444442 + 1.333333333p + p2 = -22.2222222258 Factor a perfect square on the left side: (p + 0.6666666665)(p + 0.6666666665) = -22.2222222258 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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