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Simplifying 700 = p(5p + -1) Reorder the terms: 700 = p(-1 + 5p) 700 = (-1 * p + 5p * p) 700 = (-1p + 5p2) Solving 700 = -1p + 5p2 Solving for variable 'p'. Reorder the terms: 700 + p + -5p2 = -1p + p + 5p2 + -5p2 Combine like terms: -1p + p = 0 700 + p + -5p2 = 0 + 5p2 + -5p2 700 + p + -5p2 = 5p2 + -5p2 Combine like terms: 5p2 + -5p2 = 0 700 + p + -5p2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -140 + -0.2p + p2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + -0.2p + 140 + p2 = 0 + 140 Reorder the terms: -140 + 140 + -0.2p + p2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -0.2p + p2 = 0 + 140 -0.2p + p2 = 0 + 140 Combine like terms: 0 + 140 = 140 -0.2p + p2 = 140 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. -0.2p + 0.25 + p2 = 140 + 0.25 Reorder the terms: 0.25 + -0.2p + p2 = 140 + 0.25 Combine like terms: 140 + 0.25 = 140.25 0.25 + -0.2p + p2 = 140.25 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (p + 0.5) equal to 11.842719282 and -11.842719282.Subproblem 1
p + 0.5 = 11.842719282 Simplifying p + 0.5 = 11.842719282 Reorder the terms: 0.5 + p = 11.842719282 Solving 0.5 + p = 11.842719282 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 11.842719282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 11.842719282 + -0.5 p = 11.842719282 + -0.5 Combine like terms: 11.842719282 + -0.5 = 11.342719282 p = 11.342719282 Simplifying p = 11.342719282Subproblem 2
p + 0.5 = -11.842719282 Simplifying p + 0.5 = -11.842719282 Reorder the terms: 0.5 + p = -11.842719282 Solving 0.5 + p = -11.842719282 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -11.842719282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -11.842719282 + -0.5 p = -11.842719282 + -0.5 Combine like terms: -11.842719282 + -0.5 = -12.342719282 p = -12.342719282 Simplifying p = -12.342719282Solution
The solution to the problem is based on the solutions from the subproblems. p = {11.342719282, -12.342719282}
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