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Simplifying p2 + 6p + -71 = -7 Reorder the terms: -71 + 6p + p2 = -7 Solving -71 + 6p + p2 = -7 Solving for variable 'p'. Reorder the terms: -71 + 7 + 6p + p2 = -7 + 7 Combine like terms: -71 + 7 = -64 -64 + 6p + p2 = -7 + 7 Combine like terms: -7 + 7 = 0 -64 + 6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 6p + 64 + p2 = 0 + 64 Reorder the terms: -64 + 64 + 6p + p2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 6p + p2 = 0 + 64 6p + p2 = 0 + 64 Combine like terms: 0 + 64 = 64 6p + p2 = 64 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = 64 + 9 Reorder the terms: 9 + 6p + p2 = 64 + 9 Combine like terms: 64 + 9 = 73 9 + 6p + p2 = 73 Factor a perfect square on the left side: (p + 3)(p + 3) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (p + 3) equal to 8.544003745 and -8.544003745.Subproblem 1
p + 3 = 8.544003745 Simplifying p + 3 = 8.544003745 Reorder the terms: 3 + p = 8.544003745 Solving 3 + p = 8.544003745 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + p = 8.544003745 + -3 p = 8.544003745 + -3 Combine like terms: 8.544003745 + -3 = 5.544003745 p = 5.544003745 Simplifying p = 5.544003745Subproblem 2
p + 3 = -8.544003745 Simplifying p + 3 = -8.544003745 Reorder the terms: 3 + p = -8.544003745 Solving 3 + p = -8.544003745 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + p = -8.544003745 + -3 p = -8.544003745 + -3 Combine like terms: -8.544003745 + -3 = -11.544003745 p = -11.544003745 Simplifying p = -11.544003745Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.544003745, -11.544003745}
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