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Simplifying 0 = -5p2 + 100p + -3000 Reorder the terms: 0 = -3000 + 100p + -5p2 Solving 0 = -3000 + 100p + -5p2 Solving for variable 'p'. Combine like terms: 0 + 3000 = 3000 3000 + -100p + 5p2 = -3000 + 100p + -5p2 + 3000 + -100p + 5p2 Reorder the terms: 3000 + -100p + 5p2 = -3000 + 3000 + 100p + -100p + -5p2 + 5p2 Combine like terms: -3000 + 3000 = 0 3000 + -100p + 5p2 = 0 + 100p + -100p + -5p2 + 5p2 3000 + -100p + 5p2 = 100p + -100p + -5p2 + 5p2 Combine like terms: 100p + -100p = 0 3000 + -100p + 5p2 = 0 + -5p2 + 5p2 3000 + -100p + 5p2 = -5p2 + 5p2 Combine like terms: -5p2 + 5p2 = 0 3000 + -100p + 5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(600 + -20p + p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(600 + -20p + p2)' equal to zero and attempt to solve: Simplifying 600 + -20p + p2 = 0 Solving 600 + -20p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-600' to each side of the equation. 600 + -20p + -600 + p2 = 0 + -600 Reorder the terms: 600 + -600 + -20p + p2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -20p + p2 = 0 + -600 -20p + p2 = 0 + -600 Combine like terms: 0 + -600 = -600 -20p + p2 = -600 The p term is -20p. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20p + 100 + p2 = -600 + 100 Reorder the terms: 100 + -20p + p2 = -600 + 100 Combine like terms: -600 + 100 = -500 100 + -20p + p2 = -500 Factor a perfect square on the left side: (p + -10)(p + -10) = -500 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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