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Simplifying 0 = p2 + 10p + -225 Reorder the terms: 0 = -225 + 10p + p2 Solving 0 = -225 + 10p + p2 Solving for variable 'p'. Combine like terms: 0 + 225 = 225 225 + -10p + -1p2 = -225 + 10p + p2 + 225 + -10p + -1p2 Reorder the terms: 225 + -10p + -1p2 = -225 + 225 + 10p + -10p + p2 + -1p2 Combine like terms: -225 + 225 = 0 225 + -10p + -1p2 = 0 + 10p + -10p + p2 + -1p2 225 + -10p + -1p2 = 10p + -10p + p2 + -1p2 Combine like terms: 10p + -10p = 0 225 + -10p + -1p2 = 0 + p2 + -1p2 225 + -10p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 225 + -10p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -225 + 10p + p2 = 0 Move the constant term to the right: Add '225' to each side of the equation. -225 + 10p + 225 + p2 = 0 + 225 Reorder the terms: -225 + 225 + 10p + p2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 10p + p2 = 0 + 225 10p + p2 = 0 + 225 Combine like terms: 0 + 225 = 225 10p + p2 = 225 The p term is 10p. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10p + 25 + p2 = 225 + 25 Reorder the terms: 25 + 10p + p2 = 225 + 25 Combine like terms: 225 + 25 = 250 25 + 10p + p2 = 250 Factor a perfect square on the left side: (p + 5)(p + 5) = 250 Calculate the square root of the right side: 15.811388301 Break this problem into two subproblems by setting (p + 5) equal to 15.811388301 and -15.811388301.Subproblem 1
p + 5 = 15.811388301 Simplifying p + 5 = 15.811388301 Reorder the terms: 5 + p = 15.811388301 Solving 5 + p = 15.811388301 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = 15.811388301 + -5 Combine like terms: 5 + -5 = 0 0 + p = 15.811388301 + -5 p = 15.811388301 + -5 Combine like terms: 15.811388301 + -5 = 10.811388301 p = 10.811388301 Simplifying p = 10.811388301Subproblem 2
p + 5 = -15.811388301 Simplifying p + 5 = -15.811388301 Reorder the terms: 5 + p = -15.811388301 Solving 5 + p = -15.811388301 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = -15.811388301 + -5 Combine like terms: 5 + -5 = 0 0 + p = -15.811388301 + -5 p = -15.811388301 + -5 Combine like terms: -15.811388301 + -5 = -20.811388301 p = -20.811388301 Simplifying p = -20.811388301Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.811388301, -20.811388301}
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