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Simplifying -4p2 + 168p + -295 = 0 Reorder the terms: -295 + 168p + -4p2 = 0 Solving -295 + 168p + -4p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 73.75 + -42p + p2 = 0 Move the constant term to the right: Add '-73.75' to each side of the equation. 73.75 + -42p + -73.75 + p2 = 0 + -73.75 Reorder the terms: 73.75 + -73.75 + -42p + p2 = 0 + -73.75 Combine like terms: 73.75 + -73.75 = 0.00 0.00 + -42p + p2 = 0 + -73.75 -42p + p2 = 0 + -73.75 Combine like terms: 0 + -73.75 = -73.75 -42p + p2 = -73.75 The p term is -42p. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42p + 441 + p2 = -73.75 + 441 Reorder the terms: 441 + -42p + p2 = -73.75 + 441 Combine like terms: -73.75 + 441 = 367.25 441 + -42p + p2 = 367.25 Factor a perfect square on the left side: (p + -21)(p + -21) = 367.25 Calculate the square root of the right side: 19.163767897 Break this problem into two subproblems by setting (p + -21) equal to 19.163767897 and -19.163767897.Subproblem 1
p + -21 = 19.163767897 Simplifying p + -21 = 19.163767897 Reorder the terms: -21 + p = 19.163767897 Solving -21 + p = 19.163767897 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + p = 19.163767897 + 21 Combine like terms: -21 + 21 = 0 0 + p = 19.163767897 + 21 p = 19.163767897 + 21 Combine like terms: 19.163767897 + 21 = 40.163767897 p = 40.163767897 Simplifying p = 40.163767897Subproblem 2
p + -21 = -19.163767897 Simplifying p + -21 = -19.163767897 Reorder the terms: -21 + p = -19.163767897 Solving -21 + p = -19.163767897 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + p = -19.163767897 + 21 Combine like terms: -21 + 21 = 0 0 + p = -19.163767897 + 21 p = -19.163767897 + 21 Combine like terms: -19.163767897 + 21 = 1.836232103 p = 1.836232103 Simplifying p = 1.836232103Solution
The solution to the problem is based on the solutions from the subproblems. p = {40.163767897, 1.836232103}
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