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Simplifying -2p2 = 3p + 54 Reorder the terms: -2p2 = 54 + 3p Solving -2p2 = 54 + 3p Solving for variable 'p'. Reorder the terms: -54 + -3p + -2p2 = 54 + 3p + -54 + -3p Reorder the terms: -54 + -3p + -2p2 = 54 + -54 + 3p + -3p Combine like terms: 54 + -54 = 0 -54 + -3p + -2p2 = 0 + 3p + -3p -54 + -3p + -2p2 = 3p + -3p Combine like terms: 3p + -3p = 0 -54 + -3p + -2p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(54 + 3p + 2p2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(54 + 3p + 2p2)' equal to zero and attempt to solve: Simplifying 54 + 3p + 2p2 = 0 Solving 54 + 3p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 27 + 1.5p + p2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + 1.5p + -27 + p2 = 0 + -27 Reorder the terms: 27 + -27 + 1.5p + p2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 1.5p + p2 = 0 + -27 1.5p + p2 = 0 + -27 Combine like terms: 0 + -27 = -27 1.5p + p2 = -27 The p term is 1.5p. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5p + 0.5625 + p2 = -27 + 0.5625 Reorder the terms: 0.5625 + 1.5p + p2 = -27 + 0.5625 Combine like terms: -27 + 0.5625 = -26.4375 0.5625 + 1.5p + p2 = -26.4375 Factor a perfect square on the left side: (p + 0.75)(p + 0.75) = -26.4375 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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