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Simplifying 8p2 + 8p + 1 = 0 Reorder the terms: 1 + 8p + 8p2 = 0 Solving 1 + 8p + 8p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + p + p2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + p + -0.125 + p2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + p + p2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + p + p2 = 0 + -0.125 p + p2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 p + p2 = -0.125 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. + 0.25 + p2 = -0.125 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + p2 = -0.125 + 0.25 Combine like terms: -0.125 + 0.25 = 0.125 1.25 + p2 = 0.125 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (p + 0.5) equal to 0.353553391 and -0.353553391.Subproblem 1
p + 0.5 = 0.353553391 Simplifying p + 0.5 = 0.353553391 Reorder the terms: 0.5 + p = 0.353553391 Solving 0.5 + p = 0.353553391 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 = 0.353553391 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 0.353553391 + -0.5 p = 0.353553391 + -0.5 Combine like terms: 0.353553391 + -0.5 = -0.146446609 p = -0.146446609 Simplifying p = -0.146446609Subproblem 2
p + 0.5 = -0.353553391 Simplifying p + 0.5 = -0.353553391 Reorder the terms: 0.5 + p = -0.353553391 Solving 0.5 + p = -0.353553391 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 = -0.353553391 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -0.353553391 + -0.5 p = -0.353553391 + -0.5 Combine like terms: -0.353553391 + -0.5 = -0.853553391 p = -0.853553391 Simplifying p = -0.853553391Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.146446609, -0.853553391}
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