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Simplifying 5p2 + -4p + -20 = 0 Reorder the terms: -20 + -4p + 5p2 = 0 Solving -20 + -4p + 5p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + -0.8p + p2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.8p + 4 + p2 = 0 + 4 Reorder the terms: -4 + 4 + -0.8p + p2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.8p + p2 = 0 + 4 -0.8p + p2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.8p + p2 = 4 The p term is -0.8p. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8p + 0.16 + p2 = 4 + 0.16 Reorder the terms: 0.16 + -0.8p + p2 = 4 + 0.16 Combine like terms: 4 + 0.16 = 4.16 0.16 + -0.8p + p2 = 4.16 Factor a perfect square on the left side: (p + -0.4)(p + -0.4) = 4.16 Calculate the square root of the right side: 2.039607805 Break this problem into two subproblems by setting (p + -0.4) equal to 2.039607805 and -2.039607805.Subproblem 1
p + -0.4 = 2.039607805 Simplifying p + -0.4 = 2.039607805 Reorder the terms: -0.4 + p = 2.039607805 Solving -0.4 + p = 2.039607805 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + p = 2.039607805 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + p = 2.039607805 + 0.4 p = 2.039607805 + 0.4 Combine like terms: 2.039607805 + 0.4 = 2.439607805 p = 2.439607805 Simplifying p = 2.439607805Subproblem 2
p + -0.4 = -2.039607805 Simplifying p + -0.4 = -2.039607805 Reorder the terms: -0.4 + p = -2.039607805 Solving -0.4 + p = -2.039607805 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + p = -2.039607805 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + p = -2.039607805 + 0.4 p = -2.039607805 + 0.4 Combine like terms: -2.039607805 + 0.4 = -1.639607805 p = -1.639607805 Simplifying p = -1.639607805Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.439607805, -1.639607805}
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