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Simplifying 5p2 + 10p + -8 = -9 Reorder the terms: -8 + 10p + 5p2 = -9 Solving -8 + 10p + 5p2 = -9 Solving for variable 'p'. Reorder the terms: -8 + 9 + 10p + 5p2 = -9 + 9 Combine like terms: -8 + 9 = 1 1 + 10p + 5p2 = -9 + 9 Combine like terms: -9 + 9 = 0 1 + 10p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 2p + p2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 2p + -0.2 + p2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 2p + p2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 2p + p2 = 0 + -0.2 2p + p2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 2p + p2 = -0.2 The p term is 2p. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2p + 1 + p2 = -0.2 + 1 Reorder the terms: 1 + 2p + p2 = -0.2 + 1 Combine like terms: -0.2 + 1 = 0.8 1 + 2p + p2 = 0.8 Factor a perfect square on the left side: (p + 1)(p + 1) = 0.8 Calculate the square root of the right side: 0.894427191 Break this problem into two subproblems by setting (p + 1) equal to 0.894427191 and -0.894427191.Subproblem 1
p + 1 = 0.894427191 Simplifying p + 1 = 0.894427191 Reorder the terms: 1 + p = 0.894427191 Solving 1 + p = 0.894427191 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 0.894427191 + -1 Combine like terms: 1 + -1 = 0 0 + p = 0.894427191 + -1 p = 0.894427191 + -1 Combine like terms: 0.894427191 + -1 = -0.105572809 p = -0.105572809 Simplifying p = -0.105572809Subproblem 2
p + 1 = -0.894427191 Simplifying p + 1 = -0.894427191 Reorder the terms: 1 + p = -0.894427191 Solving 1 + p = -0.894427191 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = -0.894427191 + -1 Combine like terms: 1 + -1 = 0 0 + p = -0.894427191 + -1 p = -0.894427191 + -1 Combine like terms: -0.894427191 + -1 = -1.894427191 p = -1.894427191 Simplifying p = -1.894427191Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.105572809, -1.894427191}
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