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Simplifying 5p2 + 2 = 1 + -7p Reorder the terms: 2 + 5p2 = 1 + -7p Solving 2 + 5p2 = 1 + -7p Solving for variable 'p'. Reorder the terms: 2 + -1 + 7p + 5p2 = 1 + -7p + -1 + 7p Combine like terms: 2 + -1 = 1 1 + 7p + 5p2 = 1 + -7p + -1 + 7p Reorder the terms: 1 + 7p + 5p2 = 1 + -1 + -7p + 7p Combine like terms: 1 + -1 = 0 1 + 7p + 5p2 = 0 + -7p + 7p 1 + 7p + 5p2 = -7p + 7p Combine like terms: -7p + 7p = 0 1 + 7p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 1.4p + p2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 1.4p + -0.2 + p2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 1.4p + p2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 1.4p + p2 = 0 + -0.2 1.4p + p2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 1.4p + p2 = -0.2 The p term is 1.4p. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4p + 0.49 + p2 = -0.2 + 0.49 Reorder the terms: 0.49 + 1.4p + p2 = -0.2 + 0.49 Combine like terms: -0.2 + 0.49 = 0.29 0.49 + 1.4p + p2 = 0.29 Factor a perfect square on the left side: (p + 0.7)(p + 0.7) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (p + 0.7) equal to 0.538516481 and -0.538516481.Subproblem 1
p + 0.7 = 0.538516481 Simplifying p + 0.7 = 0.538516481 Reorder the terms: 0.7 + p = 0.538516481 Solving 0.7 + p = 0.538516481 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + p = 0.538516481 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + p = 0.538516481 + -0.7 p = 0.538516481 + -0.7 Combine like terms: 0.538516481 + -0.7 = -0.161483519 p = -0.161483519 Simplifying p = -0.161483519Subproblem 2
p + 0.7 = -0.538516481 Simplifying p + 0.7 = -0.538516481 Reorder the terms: 0.7 + p = -0.538516481 Solving 0.7 + p = -0.538516481 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + p = -0.538516481 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + p = -0.538516481 + -0.7 p = -0.538516481 + -0.7 Combine like terms: -0.538516481 + -0.7 = -1.238516481 p = -1.238516481 Simplifying p = -1.238516481Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.161483519, -1.238516481}
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