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Simplifying p2 + 6p + -73 = 0 Reorder the terms: -73 + 6p + p2 = 0 Solving -73 + 6p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + 6p + 73 + p2 = 0 + 73 Reorder the terms: -73 + 73 + 6p + p2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + 6p + p2 = 0 + 73 6p + p2 = 0 + 73 Combine like terms: 0 + 73 = 73 6p + p2 = 73 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 = 73 + 9 Reorder the terms: 9 + 6p + p2 = 73 + 9 Combine like terms: 73 + 9 = 82 9 + 6p + p2 = 82 Factor a perfect square on the left side: (p + 3)(p + 3) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (p + 3) equal to 9.055385138 and -9.055385138.Subproblem 1
p + 3 = 9.055385138 Simplifying p + 3 = 9.055385138 Reorder the terms: 3 + p = 9.055385138 Solving 3 + p = 9.055385138 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 = 9.055385138 + -3 Combine like terms: 3 + -3 = 0 0 + p = 9.055385138 + -3 p = 9.055385138 + -3 Combine like terms: 9.055385138 + -3 = 6.055385138 p = 6.055385138 Simplifying p = 6.055385138Subproblem 2
p + 3 = -9.055385138 Simplifying p + 3 = -9.055385138 Reorder the terms: 3 + p = -9.055385138 Solving 3 + p = -9.055385138 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 = -9.055385138 + -3 Combine like terms: 3 + -3 = 0 0 + p = -9.055385138 + -3 p = -9.055385138 + -3 Combine like terms: -9.055385138 + -3 = -12.055385138 p = -12.055385138 Simplifying p = -12.055385138Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.055385138, -12.055385138}
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