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Simplifying 2p2 = 6p + -20 Reorder the terms: 2p2 = -20 + 6p Solving 2p2 = -20 + 6p Solving for variable 'p'. Reorder the terms: 20 + -6p + 2p2 = -20 + 6p + 20 + -6p Reorder the terms: 20 + -6p + 2p2 = -20 + 20 + 6p + -6p Combine like terms: -20 + 20 = 0 20 + -6p + 2p2 = 0 + 6p + -6p 20 + -6p + 2p2 = 6p + -6p Combine like terms: 6p + -6p = 0 20 + -6p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -3p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + -3p + p2)' equal to zero and attempt to solve: Simplifying 10 + -3p + p2 = 0 Solving 10 + -3p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -3p + -10 + p2 = 0 + -10 Reorder the terms: 10 + -10 + -3p + p2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3p + p2 = 0 + -10 -3p + p2 = 0 + -10 Combine like terms: 0 + -10 = -10 -3p + p2 = -10 The p term is -3p. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3p + 2.25 + p2 = -10 + 2.25 Reorder the terms: 2.25 + -3p + p2 = -10 + 2.25 Combine like terms: -10 + 2.25 = -7.75 2.25 + -3p + p2 = -7.75 Factor a perfect square on the left side: (p + -1.5)(p + -1.5) = -7.75 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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