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Simplifying p2 + 22p = 29 Reorder the terms: 22p + p2 = 29 Solving 22p + p2 = 29 Solving for variable 'p'. Reorder the terms: -29 + 22p + p2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 22p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 22p + 29 + p2 = 0 + 29 Reorder the terms: -29 + 29 + 22p + p2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 22p + p2 = 0 + 29 22p + p2 = 0 + 29 Combine like terms: 0 + 29 = 29 22p + p2 = 29 The p term is 22p. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22p + 121 + p2 = 29 + 121 Reorder the terms: 121 + 22p + p2 = 29 + 121 Combine like terms: 29 + 121 = 150 121 + 22p + p2 = 150 Factor a perfect square on the left side: (p + 11)(p + 11) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (p + 11) equal to 12.247448714 and -12.247448714.Subproblem 1
p + 11 = 12.247448714 Simplifying p + 11 = 12.247448714 Reorder the terms: 11 + p = 12.247448714 Solving 11 + p = 12.247448714 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + p = 12.247448714 + -11 Combine like terms: 11 + -11 = 0 0 + p = 12.247448714 + -11 p = 12.247448714 + -11 Combine like terms: 12.247448714 + -11 = 1.247448714 p = 1.247448714 Simplifying p = 1.247448714Subproblem 2
p + 11 = -12.247448714 Simplifying p + 11 = -12.247448714 Reorder the terms: 11 + p = -12.247448714 Solving 11 + p = -12.247448714 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + p = -12.247448714 + -11 Combine like terms: 11 + -11 = 0 0 + p = -12.247448714 + -11 p = -12.247448714 + -11 Combine like terms: -12.247448714 + -11 = -23.247448714 p = -23.247448714 Simplifying p = -23.247448714Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.247448714, -23.247448714}
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