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Simplifying 0 = 2p2 + 10p + 62 Reorder the terms: 0 = 62 + 10p + 2p2 Solving 0 = 62 + 10p + 2p2 Solving for variable 'p'. Combine like terms: 0 + -62 = -62 -62 + -10p + -2p2 = 62 + 10p + 2p2 + -62 + -10p + -2p2 Reorder the terms: -62 + -10p + -2p2 = 62 + -62 + 10p + -10p + 2p2 + -2p2 Combine like terms: 62 + -62 = 0 -62 + -10p + -2p2 = 0 + 10p + -10p + 2p2 + -2p2 -62 + -10p + -2p2 = 10p + -10p + 2p2 + -2p2 Combine like terms: 10p + -10p = 0 -62 + -10p + -2p2 = 0 + 2p2 + -2p2 -62 + -10p + -2p2 = 2p2 + -2p2 Combine like terms: 2p2 + -2p2 = 0 -62 + -10p + -2p2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(31 + 5p + p2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(31 + 5p + p2)' equal to zero and attempt to solve: Simplifying 31 + 5p + p2 = 0 Solving 31 + 5p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 5p + -31 + p2 = 0 + -31 Reorder the terms: 31 + -31 + 5p + p2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 5p + p2 = 0 + -31 5p + p2 = 0 + -31 Combine like terms: 0 + -31 = -31 5p + p2 = -31 The p term is 5p. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5p + 6.25 + p2 = -31 + 6.25 Reorder the terms: 6.25 + 5p + p2 = -31 + 6.25 Combine like terms: -31 + 6.25 = -24.75 6.25 + 5p + p2 = -24.75 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = -24.75 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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