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Simplifying 5p2 + 10 = 16p Reorder the terms: 10 + 5p2 = 16p Solving 10 + 5p2 = 16p Solving for variable 'p'. Reorder the terms: 10 + -16p + 5p2 = 16p + -16p Combine like terms: 16p + -16p = 0 10 + -16p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + -3.2p + p2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.2p + -2 + p2 = 0 + -2 Reorder the terms: 2 + -2 + -3.2p + p2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.2p + p2 = 0 + -2 -3.2p + p2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.2p + p2 = -2 The p term is -3.2p. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2p + 2.56 + p2 = -2 + 2.56 Reorder the terms: 2.56 + -3.2p + p2 = -2 + 2.56 Combine like terms: -2 + 2.56 = 0.56 2.56 + -3.2p + p2 = 0.56 Factor a perfect square on the left side: (p + -1.6)(p + -1.6) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (p + -1.6) equal to 0.748331477 and -0.748331477.Subproblem 1
p + -1.6 = 0.748331477 Simplifying p + -1.6 = 0.748331477 Reorder the terms: -1.6 + p = 0.748331477 Solving -1.6 + p = 0.748331477 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + p = 0.748331477 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + p = 0.748331477 + 1.6 p = 0.748331477 + 1.6 Combine like terms: 0.748331477 + 1.6 = 2.348331477 p = 2.348331477 Simplifying p = 2.348331477Subproblem 2
p + -1.6 = -0.748331477 Simplifying p + -1.6 = -0.748331477 Reorder the terms: -1.6 + p = -0.748331477 Solving -1.6 + p = -0.748331477 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + p = -0.748331477 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + p = -0.748331477 + 1.6 p = -0.748331477 + 1.6 Combine like terms: -0.748331477 + 1.6 = 0.851668523 p = 0.851668523 Simplifying p = 0.851668523Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.348331477, 0.851668523}
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