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Simplifying 2(p + 6) * p = 11 Reorder the terms: 2(6 + p) * p = 11 Reorder the terms for easier multiplication: 2p(6 + p) = 11 (6 * 2p + p * 2p) = 11 (12p + 2p2) = 11 Solving 12p + 2p2 = 11 Solving for variable 'p'. Reorder the terms: -11 + 12p + 2p2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 12p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 6p + p2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 6p + 5.5 + p2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 6p + p2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 6p + p2 = 0 + 5.5 6p + p2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 6p + p2 = 5.5 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 = 5.5 + 9 Reorder the terms: 9 + 6p + p2 = 5.5 + 9 Combine like terms: 5.5 + 9 = 14.5 9 + 6p + p2 = 14.5 Factor a perfect square on the left side: (p + 3)(p + 3) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (p + 3) equal to 3.807886553 and -3.807886553.Subproblem 1
p + 3 = 3.807886553 Simplifying p + 3 = 3.807886553 Reorder the terms: 3 + p = 3.807886553 Solving 3 + p = 3.807886553 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 = 3.807886553 + -3 Combine like terms: 3 + -3 = 0 0 + p = 3.807886553 + -3 p = 3.807886553 + -3 Combine like terms: 3.807886553 + -3 = 0.807886553 p = 0.807886553 Simplifying p = 0.807886553Subproblem 2
p + 3 = -3.807886553 Simplifying p + 3 = -3.807886553 Reorder the terms: 3 + p = -3.807886553 Solving 3 + p = -3.807886553 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 = -3.807886553 + -3 Combine like terms: 3 + -3 = 0 0 + p = -3.807886553 + -3 p = -3.807886553 + -3 Combine like terms: -3.807886553 + -3 = -6.807886553 p = -6.807886553 Simplifying p = -6.807886553Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.807886553, -6.807886553}
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