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Simplifying p2 + -10p + -225 = 0 Reorder the terms: -225 + -10p + p2 = 0 Solving -225 + -10p + p2 = 0 Solving for variable 'p'. Begin completing the square. 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 = 20.811388301 p = 20.811388301 Simplifying p = 20.811388301Subproblem 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 = -10.811388301 p = -10.811388301 Simplifying p = -10.811388301Solution
The solution to the problem is based on the solutions from the subproblems. p = {20.811388301, -10.811388301}
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