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Simplifying 1p2 + 5.92p + -5 = 0 Reorder the terms: -5 + 5.92p + 1p2 = 0 Solving -5 + 5.92p + 1p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 5.92p + 5 + p2 = 0 + 5 Reorder the terms: -5 + 5 + 5.92p + p2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 5.92p + p2 = 0 + 5 5.92p + p2 = 0 + 5 Combine like terms: 0 + 5 = 5 5.92p + p2 = 5 The p term is 5.92p. Take half its coefficient (2.96). Square it (8.7616) and add it to both sides. Add '8.7616' to each side of the equation. 5.92p + 8.7616 + p2 = 5 + 8.7616 Reorder the terms: 8.7616 + 5.92p + p2 = 5 + 8.7616 Combine like terms: 5 + 8.7616 = 13.7616 8.7616 + 5.92p + p2 = 13.7616 Factor a perfect square on the left side: (p + 2.96)(p + 2.96) = 13.7616 Calculate the square root of the right side: 3.709663057 Break this problem into two subproblems by setting (p + 2.96) equal to 3.709663057 and -3.709663057.Subproblem 1
p + 2.96 = 3.709663057 Simplifying p + 2.96 = 3.709663057 Reorder the terms: 2.96 + p = 3.709663057 Solving 2.96 + p = 3.709663057 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.96' to each side of the equation. 2.96 + -2.96 + p = 3.709663057 + -2.96 Combine like terms: 2.96 + -2.96 = 0.00 0.00 + p = 3.709663057 + -2.96 p = 3.709663057 + -2.96 Combine like terms: 3.709663057 + -2.96 = 0.749663057 p = 0.749663057 Simplifying p = 0.749663057Subproblem 2
p + 2.96 = -3.709663057 Simplifying p + 2.96 = -3.709663057 Reorder the terms: 2.96 + p = -3.709663057 Solving 2.96 + p = -3.709663057 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.96' to each side of the equation. 2.96 + -2.96 + p = -3.709663057 + -2.96 Combine like terms: 2.96 + -2.96 = 0.00 0.00 + p = -3.709663057 + -2.96 p = -3.709663057 + -2.96 Combine like terms: -3.709663057 + -2.96 = -6.669663057 p = -6.669663057 Simplifying p = -6.669663057Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.749663057, -6.669663057}
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