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Simplifying 40p + 3 * 1.49p * p = 257 Multiply 3 * 1.49 40p + 4.47p * p = 257 Multiply p * p 40p + 4.47p2 = 257 Solving 40p + 4.47p2 = 257 Solving for variable 'p'. Reorder the terms: -257 + 40p + 4.47p2 = 257 + -257 Combine like terms: 257 + -257 = 0 -257 + 40p + 4.47p2 = 0 Begin completing the square. Divide all terms by 4.47 the coefficient of the squared term: Divide each side by '4.47'. -57.49440716 + 8.948545861p + p2 = 0 Move the constant term to the right: Add '57.49440716' to each side of the equation. -57.49440716 + 8.948545861p + 57.49440716 + p2 = 0 + 57.49440716 Reorder the terms: -57.49440716 + 57.49440716 + 8.948545861p + p2 = 0 + 57.49440716 Combine like terms: -57.49440716 + 57.49440716 = 0.00000000 0.00000000 + 8.948545861p + p2 = 0 + 57.49440716 8.948545861p + p2 = 0 + 57.49440716 Combine like terms: 0 + 57.49440716 = 57.49440716 8.948545861p + p2 = 57.49440716 The p term is 8.948545861p. Take half its coefficient (4.474272931). Square it (20.01911826) and add it to both sides. Add '20.01911826' to each side of the equation. 8.948545861p + 20.01911826 + p2 = 57.49440716 + 20.01911826 Reorder the terms: 20.01911826 + 8.948545861p + p2 = 57.49440716 + 20.01911826 Combine like terms: 57.49440716 + 20.01911826 = 77.51352542 20.01911826 + 8.948545861p + p2 = 77.51352542 Factor a perfect square on the left side: (p + 4.474272931)(p + 4.474272931) = 77.51352542 Calculate the square root of the right side: 8.80417659 Break this problem into two subproblems by setting (p + 4.474272931) equal to 8.80417659 and -8.80417659.Subproblem 1
p + 4.474272931 = 8.80417659 Simplifying p + 4.474272931 = 8.80417659 Reorder the terms: 4.474272931 + p = 8.80417659 Solving 4.474272931 + p = 8.80417659 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.474272931' to each side of the equation. 4.474272931 + -4.474272931 + p = 8.80417659 + -4.474272931 Combine like terms: 4.474272931 + -4.474272931 = 0.000000000 0.000000000 + p = 8.80417659 + -4.474272931 p = 8.80417659 + -4.474272931 Combine like terms: 8.80417659 + -4.474272931 = 4.329903659 p = 4.329903659 Simplifying p = 4.329903659Subproblem 2
p + 4.474272931 = -8.80417659 Simplifying p + 4.474272931 = -8.80417659 Reorder the terms: 4.474272931 + p = -8.80417659 Solving 4.474272931 + p = -8.80417659 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.474272931' to each side of the equation. 4.474272931 + -4.474272931 + p = -8.80417659 + -4.474272931 Combine like terms: 4.474272931 + -4.474272931 = 0.000000000 0.000000000 + p = -8.80417659 + -4.474272931 p = -8.80417659 + -4.474272931 Combine like terms: -8.80417659 + -4.474272931 = -13.278449521 p = -13.278449521 Simplifying p = -13.278449521Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.329903659, -13.278449521}
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