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Simplifying P2 + 14P + -74 = 0 Reorder the terms: -74 + 14P + P2 = 0 Solving -74 + 14P + P2 = 0 Solving for variable 'P'. Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + 14P + 74 + P2 = 0 + 74 Reorder the terms: -74 + 74 + 14P + P2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + 14P + P2 = 0 + 74 14P + P2 = 0 + 74 Combine like terms: 0 + 74 = 74 14P + P2 = 74 The P term is 14P. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14P + 49 + P2 = 74 + 49 Reorder the terms: 49 + 14P + P2 = 74 + 49 Combine like terms: 74 + 49 = 123 49 + 14P + P2 = 123 Factor a perfect square on the left side: (P + 7)(P + 7) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (P + 7) equal to 11.090536506 and -11.090536506.Subproblem 1
P + 7 = 11.090536506 Simplifying P + 7 = 11.090536506 Reorder the terms: 7 + P = 11.090536506 Solving 7 + P = 11.090536506 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + P = 11.090536506 + -7 Combine like terms: 7 + -7 = 0 0 + P = 11.090536506 + -7 P = 11.090536506 + -7 Combine like terms: 11.090536506 + -7 = 4.090536506 P = 4.090536506 Simplifying P = 4.090536506Subproblem 2
P + 7 = -11.090536506 Simplifying P + 7 = -11.090536506 Reorder the terms: 7 + P = -11.090536506 Solving 7 + P = -11.090536506 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + P = -11.090536506 + -7 Combine like terms: 7 + -7 = 0 0 + P = -11.090536506 + -7 P = -11.090536506 + -7 Combine like terms: -11.090536506 + -7 = -18.090536506 P = -18.090536506 Simplifying P = -18.090536506Solution
The solution to the problem is based on the solutions from the subproblems. P = {4.090536506, -18.090536506}
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