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Simplifying p2 + -20p + -40 = 5 Reorder the terms: -40 + -20p + p2 = 5 Solving -40 + -20p + p2 = 5 Solving for variable 'p'. Reorder the terms: -40 + -5 + -20p + p2 = 5 + -5 Combine like terms: -40 + -5 = -45 -45 + -20p + p2 = 5 + -5 Combine like terms: 5 + -5 = 0 -45 + -20p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -20p + 45 + p2 = 0 + 45 Reorder the terms: -45 + 45 + -20p + p2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -20p + p2 = 0 + 45 -20p + p2 = 0 + 45 Combine like terms: 0 + 45 = 45 -20p + p2 = 45 The p term is -20p. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20p + 100 + p2 = 45 + 100 Reorder the terms: 100 + -20p + p2 = 45 + 100 Combine like terms: 45 + 100 = 145 100 + -20p + p2 = 145 Factor a perfect square on the left side: (p + -10)(p + -10) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (p + -10) equal to 12.041594579 and -12.041594579.Subproblem 1
p + -10 = 12.041594579 Simplifying p + -10 = 12.041594579 Reorder the terms: -10 + p = 12.041594579 Solving -10 + p = 12.041594579 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + p = 12.041594579 + 10 Combine like terms: -10 + 10 = 0 0 + p = 12.041594579 + 10 p = 12.041594579 + 10 Combine like terms: 12.041594579 + 10 = 22.041594579 p = 22.041594579 Simplifying p = 22.041594579Subproblem 2
p + -10 = -12.041594579 Simplifying p + -10 = -12.041594579 Reorder the terms: -10 + p = -12.041594579 Solving -10 + p = -12.041594579 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + p = -12.041594579 + 10 Combine like terms: -10 + 10 = 0 0 + p = -12.041594579 + 10 p = -12.041594579 + 10 Combine like terms: -12.041594579 + 10 = -2.041594579 p = -2.041594579 Simplifying p = -2.041594579Solution
The solution to the problem is based on the solutions from the subproblems. p = {22.041594579, -2.041594579}
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