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Simplifying (10 + -0.5p)(10 + -0.5p) = 0 Multiply (10 + -0.5p) * (10 + -0.5p) (10(10 + -0.5p) + -0.5p * (10 + -0.5p)) = 0 ((10 * 10 + -0.5p * 10) + -0.5p * (10 + -0.5p)) = 0 ((100 + -5p) + -0.5p * (10 + -0.5p)) = 0 (100 + -5p + (10 * -0.5p + -0.5p * -0.5p)) = 0 (100 + -5p + (-5p + 0.25p2)) = 0 Combine like terms: -5p + -5p = -10p (100 + -10p + 0.25p2) = 0 Solving 100 + -10p + 0.25p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 400 + -40p + p2 = 0 Move the constant term to the right: Add '-400' to each side of the equation. 400 + -40p + -400 + p2 = 0 + -400 Reorder the terms: 400 + -400 + -40p + p2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -40p + p2 = 0 + -400 -40p + p2 = 0 + -400 Combine like terms: 0 + -400 = -400 -40p + p2 = -400 The p term is -40p. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40p + 400 + p2 = -400 + 400 Reorder the terms: 400 + -40p + p2 = -400 + 400 Combine like terms: -400 + 400 = 0 400 + -40p + p2 = 0 Factor a perfect square on the left side: (p + -20)(p + -20) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (p + -20) equal to 0 and 0.Subproblem 1
p + -20 = 0 Simplifying p + -20 = 0 Reorder the terms: -20 + p = 0 Solving -20 + p = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + p = 0 + 20 Combine like terms: -20 + 20 = 0 0 + p = 0 + 20 p = 0 + 20 Combine like terms: 0 + 20 = 20 p = 20 Simplifying p = 20Subproblem 2
p + -20 = 0 Simplifying p + -20 = 0 Reorder the terms: -20 + p = 0 Solving -20 + p = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + p = 0 + 20 Combine like terms: -20 + 20 = 0 0 + p = 0 + 20 p = 0 + 20 Combine like terms: 0 + 20 = 20 p = 20 Simplifying p = 20Solution
The solution to the problem is based on the solutions from the subproblems. p = {20, 20}
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