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Simplifying 7p2 + -70p + 170 = 0 Reorder the terms: 170 + -70p + 7p2 = 0 Solving 170 + -70p + 7p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 24.28571429 + -10p + p2 = 0 Move the constant term to the right: Add '-24.28571429' to each side of the equation. 24.28571429 + -10p + -24.28571429 + p2 = 0 + -24.28571429 Reorder the terms: 24.28571429 + -24.28571429 + -10p + p2 = 0 + -24.28571429 Combine like terms: 24.28571429 + -24.28571429 = 0.00000000 0.00000000 + -10p + p2 = 0 + -24.28571429 -10p + p2 = 0 + -24.28571429 Combine like terms: 0 + -24.28571429 = -24.28571429 -10p + p2 = -24.28571429 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 = -24.28571429 + 25 Reorder the terms: 25 + -10p + p2 = -24.28571429 + 25 Combine like terms: -24.28571429 + 25 = 0.71428571 25 + -10p + p2 = 0.71428571 Factor a perfect square on the left side: (p + -5)(p + -5) = 0.71428571 Calculate the square root of the right side: 0.845154252 Break this problem into two subproblems by setting (p + -5) equal to 0.845154252 and -0.845154252.Subproblem 1
p + -5 = 0.845154252 Simplifying p + -5 = 0.845154252 Reorder the terms: -5 + p = 0.845154252 Solving -5 + p = 0.845154252 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 = 0.845154252 + 5 Combine like terms: -5 + 5 = 0 0 + p = 0.845154252 + 5 p = 0.845154252 + 5 Combine like terms: 0.845154252 + 5 = 5.845154252 p = 5.845154252 Simplifying p = 5.845154252Subproblem 2
p + -5 = -0.845154252 Simplifying p + -5 = -0.845154252 Reorder the terms: -5 + p = -0.845154252 Solving -5 + p = -0.845154252 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 = -0.845154252 + 5 Combine like terms: -5 + 5 = 0 0 + p = -0.845154252 + 5 p = -0.845154252 + 5 Combine like terms: -0.845154252 + 5 = 4.154845748 p = 4.154845748 Simplifying p = 4.154845748Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.845154252, 4.154845748}
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