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Simplifying 2p2 + -16p + -3 = 0 Reorder the terms: -3 + -16p + 2p2 = 0 Solving -3 + -16p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -8p + p2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -8p + 1.5 + p2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -8p + p2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -8p + p2 = 0 + 1.5 -8p + p2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -8p + p2 = 1.5 The p term is -8p. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8p + 16 + p2 = 1.5 + 16 Reorder the terms: 16 + -8p + p2 = 1.5 + 16 Combine like terms: 1.5 + 16 = 17.5 16 + -8p + p2 = 17.5 Factor a perfect square on the left side: (p + -4)(p + -4) = 17.5 Calculate the square root of the right side: 4.183300133 Break this problem into two subproblems by setting (p + -4) equal to 4.183300133 and -4.183300133.Subproblem 1
p + -4 = 4.183300133 Simplifying p + -4 = 4.183300133 Reorder the terms: -4 + p = 4.183300133 Solving -4 + p = 4.183300133 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = 4.183300133 + 4 Combine like terms: -4 + 4 = 0 0 + p = 4.183300133 + 4 p = 4.183300133 + 4 Combine like terms: 4.183300133 + 4 = 8.183300133 p = 8.183300133 Simplifying p = 8.183300133Subproblem 2
p + -4 = -4.183300133 Simplifying p + -4 = -4.183300133 Reorder the terms: -4 + p = -4.183300133 Solving -4 + p = -4.183300133 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = -4.183300133 + 4 Combine like terms: -4 + 4 = 0 0 + p = -4.183300133 + 4 p = -4.183300133 + 4 Combine like terms: -4.183300133 + 4 = -0.183300133 p = -0.183300133 Simplifying p = -0.183300133Solution
The solution to the problem is based on the solutions from the subproblems. p = {8.183300133, -0.183300133}
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