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Simplifying 9 = p2 + 18p Reorder the terms: 9 = 18p + p2 Solving 9 = 18p + p2 Solving for variable 'p'. Reorder the terms: 9 + -18p + -1p2 = 18p + -18p + p2 + -1p2 Combine like terms: 18p + -18p = 0 9 + -18p + -1p2 = 0 + p2 + -1p2 9 + -18p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 9 + -18p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 18p + p2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 18p + 9 + p2 = 0 + 9 Reorder the terms: -9 + 9 + 18p + p2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 18p + p2 = 0 + 9 18p + p2 = 0 + 9 Combine like terms: 0 + 9 = 9 18p + p2 = 9 The p term is 18p. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18p + 81 + p2 = 9 + 81 Reorder the terms: 81 + 18p + p2 = 9 + 81 Combine like terms: 9 + 81 = 90 81 + 18p + p2 = 90 Factor a perfect square on the left side: (p + 9)(p + 9) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (p + 9) equal to 9.486832981 and -9.486832981.Subproblem 1
p + 9 = 9.486832981 Simplifying p + 9 = 9.486832981 Reorder the terms: 9 + p = 9.486832981 Solving 9 + p = 9.486832981 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + p = 9.486832981 + -9 Combine like terms: 9 + -9 = 0 0 + p = 9.486832981 + -9 p = 9.486832981 + -9 Combine like terms: 9.486832981 + -9 = 0.486832981 p = 0.486832981 Simplifying p = 0.486832981Subproblem 2
p + 9 = -9.486832981 Simplifying p + 9 = -9.486832981 Reorder the terms: 9 + p = -9.486832981 Solving 9 + p = -9.486832981 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + p = -9.486832981 + -9 Combine like terms: 9 + -9 = 0 0 + p = -9.486832981 + -9 p = -9.486832981 + -9 Combine like terms: -9.486832981 + -9 = -18.486832981 p = -18.486832981 Simplifying p = -18.486832981Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.486832981, -18.486832981}
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