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Simplifying p2 + 14p + 5 = 0 Reorder the terms: 5 + 14p + p2 = 0 Solving 5 + 14p + p2 = 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 + 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 = 44 49 + 14p + p2 = 44 Factor a perfect square on the left side: (p + 7)(p + 7) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (p + 7) equal to 6.633249581 and -6.633249581.Subproblem 1
p + 7 = 6.633249581 Simplifying p + 7 = 6.633249581 Reorder the terms: 7 + p = 6.633249581 Solving 7 + p = 6.633249581 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 = 6.633249581 + -7 Combine like terms: 7 + -7 = 0 0 + p = 6.633249581 + -7 p = 6.633249581 + -7 Combine like terms: 6.633249581 + -7 = -0.366750419 p = -0.366750419 Simplifying p = -0.366750419Subproblem 2
p + 7 = -6.633249581 Simplifying p + 7 = -6.633249581 Reorder the terms: 7 + p = -6.633249581 Solving 7 + p = -6.633249581 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 = -6.633249581 + -7 Combine like terms: 7 + -7 = 0 0 + p = -6.633249581 + -7 p = -6.633249581 + -7 Combine like terms: -6.633249581 + -7 = -13.633249581 p = -13.633249581 Simplifying p = -13.633249581Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.366750419, -13.633249581}
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