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Simplifying 10p + -1p * p + -2 = 0 Multiply p * p 10p + -1p2 + -2 = 0 Reorder the terms: -2 + 10p + -1p2 = 0 Solving -2 + 10p + -1p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -10p + p2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -10p + -2 + p2 = 0 + -2 Reorder the terms: 2 + -2 + -10p + p2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -10p + p2 = 0 + -2 -10p + p2 = 0 + -2 Combine like terms: 0 + -2 = -2 -10p + p2 = -2 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 = -2 + 25 Reorder the terms: 25 + -10p + p2 = -2 + 25 Combine like terms: -2 + 25 = 23 25 + -10p + p2 = 23 Factor a perfect square on the left side: (p + -5)(p + -5) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (p + -5) equal to 4.795831523 and -4.795831523.Subproblem 1
p + -5 = 4.795831523 Simplifying p + -5 = 4.795831523 Reorder the terms: -5 + p = 4.795831523 Solving -5 + p = 4.795831523 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 = 4.795831523 + 5 Combine like terms: -5 + 5 = 0 0 + p = 4.795831523 + 5 p = 4.795831523 + 5 Combine like terms: 4.795831523 + 5 = 9.795831523 p = 9.795831523 Simplifying p = 9.795831523Subproblem 2
p + -5 = -4.795831523 Simplifying p + -5 = -4.795831523 Reorder the terms: -5 + p = -4.795831523 Solving -5 + p = -4.795831523 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 = -4.795831523 + 5 Combine like terms: -5 + 5 = 0 0 + p = -4.795831523 + 5 p = -4.795831523 + 5 Combine like terms: -4.795831523 + 5 = 0.204168477 p = 0.204168477 Simplifying p = 0.204168477Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.795831523, 0.204168477}
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