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Simplifying 4p2 + -1p + -400 = 0 Reorder the terms: -400 + -1p + 4p2 = 0 Solving -400 + -1p + 4p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -100 + -0.25p + p2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -0.25p + 100 + p2 = 0 + 100 Reorder the terms: -100 + 100 + -0.25p + p2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -0.25p + p2 = 0 + 100 -0.25p + p2 = 0 + 100 Combine like terms: 0 + 100 = 100 -0.25p + p2 = 100 The p term is -0.25p. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25p + 0.015625 + p2 = 100 + 0.015625 Reorder the terms: 0.015625 + -0.25p + p2 = 100 + 0.015625 Combine like terms: 100 + 0.015625 = 100.015625 0.015625 + -0.25p + p2 = 100.015625 Factor a perfect square on the left side: (p + -0.125)(p + -0.125) = 100.015625 Calculate the square root of the right side: 10.000781219 Break this problem into two subproblems by setting (p + -0.125) equal to 10.000781219 and -10.000781219.Subproblem 1
p + -0.125 = 10.000781219 Simplifying p + -0.125 = 10.000781219 Reorder the terms: -0.125 + p = 10.000781219 Solving -0.125 + p = 10.000781219 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + p = 10.000781219 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + p = 10.000781219 + 0.125 p = 10.000781219 + 0.125 Combine like terms: 10.000781219 + 0.125 = 10.125781219 p = 10.125781219 Simplifying p = 10.125781219Subproblem 2
p + -0.125 = -10.000781219 Simplifying p + -0.125 = -10.000781219 Reorder the terms: -0.125 + p = -10.000781219 Solving -0.125 + p = -10.000781219 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + p = -10.000781219 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + p = -10.000781219 + 0.125 p = -10.000781219 + 0.125 Combine like terms: -10.000781219 + 0.125 = -9.875781219 p = -9.875781219 Simplifying p = -9.875781219Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.125781219, -9.875781219}
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