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Simplifying 2p2 + -7 = 7p Reorder the terms: -7 + 2p2 = 7p Solving -7 + 2p2 = 7p Solving for variable 'p'. Reorder the terms: -7 + -7p + 2p2 = 7p + -7p Combine like terms: 7p + -7p = 0 -7 + -7p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -3.5p + p2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -3.5p + 3.5 + p2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -3.5p + p2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -3.5p + p2 = 0 + 3.5 -3.5p + p2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -3.5p + p2 = 3.5 The p term is -3.5p. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5p + 3.0625 + p2 = 3.5 + 3.0625 Reorder the terms: 3.0625 + -3.5p + p2 = 3.5 + 3.0625 Combine like terms: 3.5 + 3.0625 = 6.5625 3.0625 + -3.5p + p2 = 6.5625 Factor a perfect square on the left side: (p + -1.75)(p + -1.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (p + -1.75) equal to 2.561737691 and -2.561737691.Subproblem 1
p + -1.75 = 2.561737691 Simplifying p + -1.75 = 2.561737691 Reorder the terms: -1.75 + p = 2.561737691 Solving -1.75 + p = 2.561737691 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + p = 2.561737691 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + p = 2.561737691 + 1.75 p = 2.561737691 + 1.75 Combine like terms: 2.561737691 + 1.75 = 4.311737691 p = 4.311737691 Simplifying p = 4.311737691Subproblem 2
p + -1.75 = -2.561737691 Simplifying p + -1.75 = -2.561737691 Reorder the terms: -1.75 + p = -2.561737691 Solving -1.75 + p = -2.561737691 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + p = -2.561737691 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + p = -2.561737691 + 1.75 p = -2.561737691 + 1.75 Combine like terms: -2.561737691 + 1.75 = -0.811737691 p = -0.811737691 Simplifying p = -0.811737691Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.311737691, -0.811737691}
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