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Simplifying p2 + 14p + 49 = 5 + 49 Reorder the terms: 49 + 14p + p2 = 5 + 49 Combine like terms: 5 + 49 = 54 49 + 14p + p2 = 54 Solving 49 + 14p + p2 = 54 Solving for variable 'p'. Reorder the terms: 49 + -54 + 14p + p2 = 54 + -54 Combine like terms: 49 + -54 = -5 -5 + 14p + p2 = 54 + -54 Combine like terms: 54 + -54 = 0 -5 + 14p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 14p + 5 + p2 = 0 + 5 Reorder the terms: -5 + 5 + 14p + p2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 14p + p2 = 0 + 5 14p + p2 = 0 + 5 Combine like terms: 0 + 5 = 5 14p + p2 = 5 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 = 5 + 49 Reorder the terms: 49 + 14p + p2 = 5 + 49 Combine like terms: 5 + 49 = 54 49 + 14p + p2 = 54 Factor a perfect square on the left side: (p + 7)(p + 7) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (p + 7) equal to 7.348469228 and -7.348469228.Subproblem 1
p + 7 = 7.348469228 Simplifying p + 7 = 7.348469228 Reorder the terms: 7 + p = 7.348469228 Solving 7 + p = 7.348469228 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 = 7.348469228 + -7 Combine like terms: 7 + -7 = 0 0 + p = 7.348469228 + -7 p = 7.348469228 + -7 Combine like terms: 7.348469228 + -7 = 0.348469228 p = 0.348469228 Simplifying p = 0.348469228Subproblem 2
p + 7 = -7.348469228 Simplifying p + 7 = -7.348469228 Reorder the terms: 7 + p = -7.348469228 Solving 7 + p = -7.348469228 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 = -7.348469228 + -7 Combine like terms: 7 + -7 = 0 0 + p = -7.348469228 + -7 p = -7.348469228 + -7 Combine like terms: -7.348469228 + -7 = -14.348469228 p = -14.348469228 Simplifying p = -14.348469228Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.348469228, -14.348469228}
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