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Simplifying 2p4 + -4p2 + 250 = 0 Reorder the terms: 250 + -4p2 + 2p4 = 0 Solving 250 + -4p2 + 2p4 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(125 + -2p2 + p4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(125 + -2p2 + p4)' equal to zero and attempt to solve: Simplifying 125 + -2p2 + p4 = 0 Solving 125 + -2p2 + p4 = 0 Begin completing the square. Move the constant term to the right: Add '-125' to each side of the equation. 125 + -2p2 + -125 + p4 = 0 + -125 Reorder the terms: 125 + -125 + -2p2 + p4 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -2p2 + p4 = 0 + -125 -2p2 + p4 = 0 + -125 Combine like terms: 0 + -125 = -125 -2p2 + p4 = -125 The p term is -2p2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2p2 + 1 + p4 = -125 + 1 Reorder the terms: 1 + -2p2 + p4 = -125 + 1 Combine like terms: -125 + 1 = -124 1 + -2p2 + p4 = -124 Factor a perfect square on the left side: (p2 + -1)(p2 + -1) = -124 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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