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Simplifying 5p + -10p2 = 20 Solving 5p + -10p2 = 20 Solving for variable 'p'. Reorder the terms: -20 + 5p + -10p2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 5p + -10p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + p + -2p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + p + -2p2)' equal to zero and attempt to solve: Simplifying -4 + p + -2p2 = 0 Solving -4 + p + -2p2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2 + -0.5p + p2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.5p + -2 + p2 = 0 + -2 Reorder the terms: 2 + -2 + -0.5p + p2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.5p + p2 = 0 + -2 -0.5p + p2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.5p + p2 = -2 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5p + 0.25 + p2 = -2 + 0.25 Reorder the terms: 0.25 + -0.5p + p2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + -0.5p + p2 = -1.75 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = -1.75 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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