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Simplifying p2 + -10p + -46 = 0 Reorder the terms: -46 + -10p + p2 = 0 Solving -46 + -10p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -10p + 46 + p2 = 0 + 46 Reorder the terms: -46 + 46 + -10p + p2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -10p + p2 = 0 + 46 -10p + p2 = 0 + 46 Combine like terms: 0 + 46 = 46 -10p + p2 = 46 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 = 46 + 25 Reorder the terms: 25 + -10p + p2 = 46 + 25 Combine like terms: 46 + 25 = 71 25 + -10p + p2 = 71 Factor a perfect square on the left side: (p + -5)(p + -5) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (p + -5) equal to 8.426149773 and -8.426149773.Subproblem 1
p + -5 = 8.426149773 Simplifying p + -5 = 8.426149773 Reorder the terms: -5 + p = 8.426149773 Solving -5 + p = 8.426149773 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 = 8.426149773 + 5 Combine like terms: -5 + 5 = 0 0 + p = 8.426149773 + 5 p = 8.426149773 + 5 Combine like terms: 8.426149773 + 5 = 13.426149773 p = 13.426149773 Simplifying p = 13.426149773Subproblem 2
p + -5 = -8.426149773 Simplifying p + -5 = -8.426149773 Reorder the terms: -5 + p = -8.426149773 Solving -5 + p = -8.426149773 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 = -8.426149773 + 5 Combine like terms: -5 + 5 = 0 0 + p = -8.426149773 + 5 p = -8.426149773 + 5 Combine like terms: -8.426149773 + 5 = -3.426149773 p = -3.426149773 Simplifying p = -3.426149773Solution
The solution to the problem is based on the solutions from the subproblems. p = {13.426149773, -3.426149773}
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