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Simplifying p2 + 6p + -62 = -8 Reorder the terms: -62 + 6p + p2 = -8 Solving -62 + 6p + p2 = -8 Solving for variable 'p'. Reorder the terms: -62 + 8 + 6p + p2 = -8 + 8 Combine like terms: -62 + 8 = -54 -54 + 6p + p2 = -8 + 8 Combine like terms: -8 + 8 = 0 -54 + 6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 6p + 54 + p2 = 0 + 54 Reorder the terms: -54 + 54 + 6p + p2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 6p + p2 = 0 + 54 6p + p2 = 0 + 54 Combine like terms: 0 + 54 = 54 6p + p2 = 54 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 = 54 + 9 Reorder the terms: 9 + 6p + p2 = 54 + 9 Combine like terms: 54 + 9 = 63 9 + 6p + p2 = 63 Factor a perfect square on the left side: (p + 3)(p + 3) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (p + 3) equal to 7.937253933 and -7.937253933.Subproblem 1
p + 3 = 7.937253933 Simplifying p + 3 = 7.937253933 Reorder the terms: 3 + p = 7.937253933 Solving 3 + p = 7.937253933 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 = 7.937253933 + -3 Combine like terms: 3 + -3 = 0 0 + p = 7.937253933 + -3 p = 7.937253933 + -3 Combine like terms: 7.937253933 + -3 = 4.937253933 p = 4.937253933 Simplifying p = 4.937253933Subproblem 2
p + 3 = -7.937253933 Simplifying p + 3 = -7.937253933 Reorder the terms: 3 + p = -7.937253933 Solving 3 + p = -7.937253933 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 = -7.937253933 + -3 Combine like terms: 3 + -3 = 0 0 + p = -7.937253933 + -3 p = -7.937253933 + -3 Combine like terms: -7.937253933 + -3 = -10.937253933 p = -10.937253933 Simplifying p = -10.937253933Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.937253933, -10.937253933}
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