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Simplifying -5p2 = 400p + -8000 Reorder the terms: -5p2 = -8000 + 400p Solving -5p2 = -8000 + 400p Solving for variable 'p'. Reorder the terms: 8000 + -400p + -5p2 = -8000 + 400p + 8000 + -400p Reorder the terms: 8000 + -400p + -5p2 = -8000 + 8000 + 400p + -400p Combine like terms: -8000 + 8000 = 0 8000 + -400p + -5p2 = 0 + 400p + -400p 8000 + -400p + -5p2 = 400p + -400p Combine like terms: 400p + -400p = 0 8000 + -400p + -5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1600 + -80p + -1p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1600 + -80p + -1p2)' equal to zero and attempt to solve: Simplifying 1600 + -80p + -1p2 = 0 Solving 1600 + -80p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1600 + 80p + p2 = 0 Move the constant term to the right: Add '1600' to each side of the equation. -1600 + 80p + 1600 + p2 = 0 + 1600 Reorder the terms: -1600 + 1600 + 80p + p2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + 80p + p2 = 0 + 1600 80p + p2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 80p + p2 = 1600 The p term is 80p. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80p + 1600 + p2 = 1600 + 1600 Reorder the terms: 1600 + 80p + p2 = 1600 + 1600 Combine like terms: 1600 + 1600 = 3200 1600 + 80p + p2 = 3200 Factor a perfect square on the left side: (p + 40)(p + 40) = 3200 Calculate the square root of the right side: 56.568542495 Break this problem into two subproblems by setting (p + 40) equal to 56.568542495 and -56.568542495.Subproblem 1
p + 40 = 56.568542495 Simplifying p + 40 = 56.568542495 Reorder the terms: 40 + p = 56.568542495 Solving 40 + p = 56.568542495 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + p = 56.568542495 + -40 Combine like terms: 40 + -40 = 0 0 + p = 56.568542495 + -40 p = 56.568542495 + -40 Combine like terms: 56.568542495 + -40 = 16.568542495 p = 16.568542495 Simplifying p = 16.568542495Subproblem 2
p + 40 = -56.568542495 Simplifying p + 40 = -56.568542495 Reorder the terms: 40 + p = -56.568542495 Solving 40 + p = -56.568542495 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + p = -56.568542495 + -40 Combine like terms: 40 + -40 = 0 0 + p = -56.568542495 + -40 p = -56.568542495 + -40 Combine like terms: -56.568542495 + -40 = -96.568542495 p = -96.568542495 Simplifying p = -96.568542495Solution
The solution to the problem is based on the solutions from the subproblems. p = {16.568542495, -96.568542495}Solution
p = {16.568542495, -96.568542495}
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