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Simplifying -2p(p + -5) + 7p = -5 Reorder the terms: -2p(-5 + p) + 7p = -5 (-5 * -2p + p * -2p) + 7p = -5 (10p + -2p2) + 7p = -5 Reorder the terms: 10p + 7p + -2p2 = -5 Combine like terms: 10p + 7p = 17p 17p + -2p2 = -5 Solving 17p + -2p2 = -5 Solving for variable 'p'. Reorder the terms: 5 + 17p + -2p2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 17p + -2p2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + -8.5p + p2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -8.5p + 2.5 + p2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -8.5p + p2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -8.5p + p2 = 0 + 2.5 -8.5p + p2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -8.5p + p2 = 2.5 The p term is -8.5p. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5p + 18.0625 + p2 = 2.5 + 18.0625 Reorder the terms: 18.0625 + -8.5p + p2 = 2.5 + 18.0625 Combine like terms: 2.5 + 18.0625 = 20.5625 18.0625 + -8.5p + p2 = 20.5625 Factor a perfect square on the left side: (p + -4.25)(p + -4.25) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (p + -4.25) equal to 4.534589287 and -4.534589287.Subproblem 1
p + -4.25 = 4.534589287 Simplifying p + -4.25 = 4.534589287 Reorder the terms: -4.25 + p = 4.534589287 Solving -4.25 + p = 4.534589287 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + p = 4.534589287 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + p = 4.534589287 + 4.25 p = 4.534589287 + 4.25 Combine like terms: 4.534589287 + 4.25 = 8.784589287 p = 8.784589287 Simplifying p = 8.784589287Subproblem 2
p + -4.25 = -4.534589287 Simplifying p + -4.25 = -4.534589287 Reorder the terms: -4.25 + p = -4.534589287 Solving -4.25 + p = -4.534589287 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + p = -4.534589287 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + p = -4.534589287 + 4.25 p = -4.534589287 + 4.25 Combine like terms: -4.534589287 + 4.25 = -0.284589287 p = -0.284589287 Simplifying p = -0.284589287Solution
The solution to the problem is based on the solutions from the subproblems. p = {8.784589287, -0.284589287}
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