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Simplifying (p + -7) * p + -1 = 0 Reorder the terms: (-7 + p) * p + -1 = 0 Reorder the terms for easier multiplication: p(-7 + p) + -1 = 0 (-7 * p + p * p) + -1 = 0 (-7p + p2) + -1 = 0 Reorder the terms: -1 + -7p + p2 = 0 Solving -1 + -7p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -7p + 1 + p2 = 0 + 1 Reorder the terms: -1 + 1 + -7p + p2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7p + p2 = 0 + 1 -7p + p2 = 0 + 1 Combine like terms: 0 + 1 = 1 -7p + p2 = 1 The p term is -7p. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7p + 12.25 + p2 = 1 + 12.25 Reorder the terms: 12.25 + -7p + p2 = 1 + 12.25 Combine like terms: 1 + 12.25 = 13.25 12.25 + -7p + p2 = 13.25 Factor a perfect square on the left side: (p + -3.5)(p + -3.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (p + -3.5) equal to 3.640054945 and -3.640054945.Subproblem 1
p + -3.5 = 3.640054945 Simplifying p + -3.5 = 3.640054945 Reorder the terms: -3.5 + p = 3.640054945 Solving -3.5 + p = 3.640054945 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = 3.640054945 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = 3.640054945 + 3.5 p = 3.640054945 + 3.5 Combine like terms: 3.640054945 + 3.5 = 7.140054945 p = 7.140054945 Simplifying p = 7.140054945Subproblem 2
p + -3.5 = -3.640054945 Simplifying p + -3.5 = -3.640054945 Reorder the terms: -3.5 + p = -3.640054945 Solving -3.5 + p = -3.640054945 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = -3.640054945 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = -3.640054945 + 3.5 p = -3.640054945 + 3.5 Combine like terms: -3.640054945 + 3.5 = -0.140054945 p = -0.140054945 Simplifying p = -0.140054945Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.140054945, -0.140054945}
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