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Simplifying p2 + -12p + -66 = 8 Reorder the terms: -66 + -12p + p2 = 8 Solving -66 + -12p + p2 = 8 Solving for variable 'p'. Reorder the terms: -66 + -8 + -12p + p2 = 8 + -8 Combine like terms: -66 + -8 = -74 -74 + -12p + p2 = 8 + -8 Combine like terms: 8 + -8 = 0 -74 + -12p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + -12p + 74 + p2 = 0 + 74 Reorder the terms: -74 + 74 + -12p + p2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -12p + p2 = 0 + 74 -12p + p2 = 0 + 74 Combine like terms: 0 + 74 = 74 -12p + p2 = 74 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 = 74 + 36 Reorder the terms: 36 + -12p + p2 = 74 + 36 Combine like terms: 74 + 36 = 110 36 + -12p + p2 = 110 Factor a perfect square on the left side: (p + -6)(p + -6) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (p + -6) equal to 10.488088482 and -10.488088482.Subproblem 1
p + -6 = 10.488088482 Simplifying p + -6 = 10.488088482 Reorder the terms: -6 + p = 10.488088482 Solving -6 + p = 10.488088482 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 = 10.488088482 + 6 Combine like terms: -6 + 6 = 0 0 + p = 10.488088482 + 6 p = 10.488088482 + 6 Combine like terms: 10.488088482 + 6 = 16.488088482 p = 16.488088482 Simplifying p = 16.488088482Subproblem 2
p + -6 = -10.488088482 Simplifying p + -6 = -10.488088482 Reorder the terms: -6 + p = -10.488088482 Solving -6 + p = -10.488088482 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 = -10.488088482 + 6 Combine like terms: -6 + 6 = 0 0 + p = -10.488088482 + 6 p = -10.488088482 + 6 Combine like terms: -10.488088482 + 6 = -4.488088482 p = -4.488088482 Simplifying p = -4.488088482Solution
The solution to the problem is based on the solutions from the subproblems. p = {16.488088482, -4.488088482}
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