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Simplifying 2p2 + -15p + 8 = 43 Reorder the terms: 8 + -15p + 2p2 = 43 Solving 8 + -15p + 2p2 = 43 Solving for variable 'p'. Reorder the terms: 8 + -43 + -15p + 2p2 = 43 + -43 Combine like terms: 8 + -43 = -35 -35 + -15p + 2p2 = 43 + -43 Combine like terms: 43 + -43 = 0 -35 + -15p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -7.5p + p2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -7.5p + 17.5 + p2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -7.5p + p2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -7.5p + p2 = 0 + 17.5 -7.5p + p2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -7.5p + p2 = 17.5 The p term is -7.5p. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5p + 14.0625 + p2 = 17.5 + 14.0625 Reorder the terms: 14.0625 + -7.5p + p2 = 17.5 + 14.0625 Combine like terms: 17.5 + 14.0625 = 31.5625 14.0625 + -7.5p + p2 = 31.5625 Factor a perfect square on the left side: (p + -3.75)(p + -3.75) = 31.5625 Calculate the square root of the right side: 5.618051264 Break this problem into two subproblems by setting (p + -3.75) equal to 5.618051264 and -5.618051264.Subproblem 1
p + -3.75 = 5.618051264 Simplifying p + -3.75 = 5.618051264 Reorder the terms: -3.75 + p = 5.618051264 Solving -3.75 + p = 5.618051264 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + p = 5.618051264 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + p = 5.618051264 + 3.75 p = 5.618051264 + 3.75 Combine like terms: 5.618051264 + 3.75 = 9.368051264 p = 9.368051264 Simplifying p = 9.368051264Subproblem 2
p + -3.75 = -5.618051264 Simplifying p + -3.75 = -5.618051264 Reorder the terms: -3.75 + p = -5.618051264 Solving -3.75 + p = -5.618051264 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + p = -5.618051264 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + p = -5.618051264 + 3.75 p = -5.618051264 + 3.75 Combine like terms: -5.618051264 + 3.75 = -1.868051264 p = -1.868051264 Simplifying p = -1.868051264Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.368051264, -1.868051264}
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