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Simplifying 4p2 + -1p + -100 = 0 Reorder the terms: -100 + -1p + 4p2 = 0 Solving -100 + -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'. -25 + -0.25p + p2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -0.25p + 25 + p2 = 0 + 25 Reorder the terms: -25 + 25 + -0.25p + p2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -0.25p + p2 = 0 + 25 -0.25p + p2 = 0 + 25 Combine like terms: 0 + 25 = 25 -0.25p + p2 = 25 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 = 25 + 0.015625 Reorder the terms: 0.015625 + -0.25p + p2 = 25 + 0.015625 Combine like terms: 25 + 0.015625 = 25.015625 0.015625 + -0.25p + p2 = 25.015625 Factor a perfect square on the left side: (p + -0.125)(p + -0.125) = 25.015625 Calculate the square root of the right side: 5.001562256 Break this problem into two subproblems by setting (p + -0.125) equal to 5.001562256 and -5.001562256.Subproblem 1
p + -0.125 = 5.001562256 Simplifying p + -0.125 = 5.001562256 Reorder the terms: -0.125 + p = 5.001562256 Solving -0.125 + p = 5.001562256 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 = 5.001562256 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + p = 5.001562256 + 0.125 p = 5.001562256 + 0.125 Combine like terms: 5.001562256 + 0.125 = 5.126562256 p = 5.126562256 Simplifying p = 5.126562256Subproblem 2
p + -0.125 = -5.001562256 Simplifying p + -0.125 = -5.001562256 Reorder the terms: -0.125 + p = -5.001562256 Solving -0.125 + p = -5.001562256 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 = -5.001562256 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + p = -5.001562256 + 0.125 p = -5.001562256 + 0.125 Combine like terms: -5.001562256 + 0.125 = -4.876562256 p = -4.876562256 Simplifying p = -4.876562256Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.126562256, -4.876562256}
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