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Simplifying p2 + -12p + 11 = 7 Reorder the terms: 11 + -12p + p2 = 7 Solving 11 + -12p + p2 = 7 Solving for variable 'p'. Reorder the terms: 11 + -7 + -12p + p2 = 7 + -7 Combine like terms: 11 + -7 = 4 4 + -12p + p2 = 7 + -7 Combine like terms: 7 + -7 = 0 4 + -12p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -12p + -4 + p2 = 0 + -4 Reorder the terms: 4 + -4 + -12p + p2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -12p + p2 = 0 + -4 -12p + p2 = 0 + -4 Combine like terms: 0 + -4 = -4 -12p + p2 = -4 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 = -4 + 36 Reorder the terms: 36 + -12p + p2 = -4 + 36 Combine like terms: -4 + 36 = 32 36 + -12p + p2 = 32 Factor a perfect square on the left side: (p + -6)(p + -6) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (p + -6) equal to 5.656854249 and -5.656854249.Subproblem 1
p + -6 = 5.656854249 Simplifying p + -6 = 5.656854249 Reorder the terms: -6 + p = 5.656854249 Solving -6 + p = 5.656854249 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 = 5.656854249 + 6 Combine like terms: -6 + 6 = 0 0 + p = 5.656854249 + 6 p = 5.656854249 + 6 Combine like terms: 5.656854249 + 6 = 11.656854249 p = 11.656854249 Simplifying p = 11.656854249Subproblem 2
p + -6 = -5.656854249 Simplifying p + -6 = -5.656854249 Reorder the terms: -6 + p = -5.656854249 Solving -6 + p = -5.656854249 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 = -5.656854249 + 6 Combine like terms: -6 + 6 = 0 0 + p = -5.656854249 + 6 p = -5.656854249 + 6 Combine like terms: -5.656854249 + 6 = 0.343145751 p = 0.343145751 Simplifying p = 0.343145751Solution
The solution to the problem is based on the solutions from the subproblems. p = {11.656854249, 0.343145751}
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