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Simplifying 5p2 = -10p + 1 Reorder the terms: 5p2 = 1 + -10p Solving 5p2 = 1 + -10p Solving for variable 'p'. Reorder the terms: -1 + 10p + 5p2 = 1 + -10p + -1 + 10p Reorder the terms: -1 + 10p + 5p2 = 1 + -1 + -10p + 10p Combine like terms: 1 + -1 = 0 -1 + 10p + 5p2 = 0 + -10p + 10p -1 + 10p + 5p2 = -10p + 10p Combine like terms: -10p + 10p = 0 -1 + 10p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 2p + p2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 2p + 0.2 + p2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 2p + p2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 2p + p2 = 0 + 0.2 2p + p2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 2p + p2 = 0.2 The p term is 2p. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2p + 1 + p2 = 0.2 + 1 Reorder the terms: 1 + 2p + p2 = 0.2 + 1 Combine like terms: 0.2 + 1 = 1.2 1 + 2p + p2 = 1.2 Factor a perfect square on the left side: (p + 1)(p + 1) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (p + 1) equal to 1.095445115 and -1.095445115.Subproblem 1
p + 1 = 1.095445115 Simplifying p + 1 = 1.095445115 Reorder the terms: 1 + p = 1.095445115 Solving 1 + p = 1.095445115 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 1.095445115 + -1 Combine like terms: 1 + -1 = 0 0 + p = 1.095445115 + -1 p = 1.095445115 + -1 Combine like terms: 1.095445115 + -1 = 0.095445115 p = 0.095445115 Simplifying p = 0.095445115Subproblem 2
p + 1 = -1.095445115 Simplifying p + 1 = -1.095445115 Reorder the terms: 1 + p = -1.095445115 Solving 1 + p = -1.095445115 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = -1.095445115 + -1 Combine like terms: 1 + -1 = 0 0 + p = -1.095445115 + -1 p = -1.095445115 + -1 Combine like terms: -1.095445115 + -1 = -2.095445115 p = -2.095445115 Simplifying p = -2.095445115Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.095445115, -2.095445115}
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