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Simplifying p2 + 9p = 14 Reorder the terms: 9p + p2 = 14 Solving 9p + p2 = 14 Solving for variable 'p'. Reorder the terms: -14 + 9p + p2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 9p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 9p + 14 + p2 = 0 + 14 Reorder the terms: -14 + 14 + 9p + p2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 9p + p2 = 0 + 14 9p + p2 = 0 + 14 Combine like terms: 0 + 14 = 14 9p + p2 = 14 The p term is 9p. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9p + 20.25 + p2 = 14 + 20.25 Reorder the terms: 20.25 + 9p + p2 = 14 + 20.25 Combine like terms: 14 + 20.25 = 34.25 20.25 + 9p + p2 = 34.25 Factor a perfect square on the left side: (p + 4.5)(p + 4.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (p + 4.5) equal to 5.852349955 and -5.852349955.Subproblem 1
p + 4.5 = 5.852349955 Simplifying p + 4.5 = 5.852349955 Reorder the terms: 4.5 + p = 5.852349955 Solving 4.5 + p = 5.852349955 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + p = 5.852349955 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = 5.852349955 + -4.5 p = 5.852349955 + -4.5 Combine like terms: 5.852349955 + -4.5 = 1.352349955 p = 1.352349955 Simplifying p = 1.352349955Subproblem 2
p + 4.5 = -5.852349955 Simplifying p + 4.5 = -5.852349955 Reorder the terms: 4.5 + p = -5.852349955 Solving 4.5 + p = -5.852349955 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + p = -5.852349955 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = -5.852349955 + -4.5 p = -5.852349955 + -4.5 Combine like terms: -5.852349955 + -4.5 = -10.352349955 p = -10.352349955 Simplifying p = -10.352349955Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.352349955, -10.352349955}
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