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Simplifying p2 + -5p = 43 Reorder the terms: -5p + p2 = 43 Solving -5p + p2 = 43 Solving for variable 'p'. Reorder the terms: -43 + -5p + p2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -5p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -5p + 43 + p2 = 0 + 43 Reorder the terms: -43 + 43 + -5p + p2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -5p + p2 = 0 + 43 -5p + p2 = 0 + 43 Combine like terms: 0 + 43 = 43 -5p + p2 = 43 The p term is -5p. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5p + 6.25 + p2 = 43 + 6.25 Reorder the terms: 6.25 + -5p + p2 = 43 + 6.25 Combine like terms: 43 + 6.25 = 49.25 6.25 + -5p + p2 = 49.25 Factor a perfect square on the left side: (p + -2.5)(p + -2.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (p + -2.5) equal to 7.017834424 and -7.017834424.Subproblem 1
p + -2.5 = 7.017834424 Simplifying p + -2.5 = 7.017834424 Reorder the terms: -2.5 + p = 7.017834424 Solving -2.5 + p = 7.017834424 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + p = 7.017834424 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = 7.017834424 + 2.5 p = 7.017834424 + 2.5 Combine like terms: 7.017834424 + 2.5 = 9.517834424 p = 9.517834424 Simplifying p = 9.517834424Subproblem 2
p + -2.5 = -7.017834424 Simplifying p + -2.5 = -7.017834424 Reorder the terms: -2.5 + p = -7.017834424 Solving -2.5 + p = -7.017834424 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + p = -7.017834424 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = -7.017834424 + 2.5 p = -7.017834424 + 2.5 Combine like terms: -7.017834424 + 2.5 = -4.517834424 p = -4.517834424 Simplifying p = -4.517834424Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.517834424, -4.517834424}
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