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Simplifying p2 + 12p + -77 = -4 Reorder the terms: -77 + 12p + p2 = -4 Solving -77 + 12p + p2 = -4 Solving for variable 'p'. Reorder the terms: -77 + 4 + 12p + p2 = -4 + 4 Combine like terms: -77 + 4 = -73 -73 + 12p + p2 = -4 + 4 Combine like terms: -4 + 4 = 0 -73 + 12p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + 12p + 73 + p2 = 0 + 73 Reorder the terms: -73 + 73 + 12p + p2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + 12p + p2 = 0 + 73 12p + p2 = 0 + 73 Combine like terms: 0 + 73 = 73 12p + p2 = 73 The p term is 12p. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12p + 36 + p2 = 73 + 36 Reorder the terms: 36 + 12p + p2 = 73 + 36 Combine like terms: 73 + 36 = 109 36 + 12p + p2 = 109 Factor a perfect square on the left side: (p + 6)(p + 6) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (p + 6) equal to 10.440306509 and -10.440306509.Subproblem 1
p + 6 = 10.440306509 Simplifying p + 6 = 10.440306509 Reorder the terms: 6 + p = 10.440306509 Solving 6 + p = 10.440306509 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + p = 10.440306509 + -6 Combine like terms: 6 + -6 = 0 0 + p = 10.440306509 + -6 p = 10.440306509 + -6 Combine like terms: 10.440306509 + -6 = 4.440306509 p = 4.440306509 Simplifying p = 4.440306509Subproblem 2
p + 6 = -10.440306509 Simplifying p + 6 = -10.440306509 Reorder the terms: 6 + p = -10.440306509 Solving 6 + p = -10.440306509 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + p = -10.440306509 + -6 Combine like terms: 6 + -6 = 0 0 + p = -10.440306509 + -6 p = -10.440306509 + -6 Combine like terms: -10.440306509 + -6 = -16.440306509 p = -16.440306509 Simplifying p = -16.440306509Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.440306509, -16.440306509}
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