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Simplifying 0.002015 = p + -8.85p2 Solving 0.002015 = p + -8.85p2 Solving for variable 'p'. Reorder the terms: 0.002015 + -1p + 8.85p2 = p + -1p + -8.85p2 + 8.85p2 Combine like terms: p + -1p = 0 0.002015 + -1p + 8.85p2 = 0 + -8.85p2 + 8.85p2 0.002015 + -1p + 8.85p2 = -8.85p2 + 8.85p2 Combine like terms: -8.85p2 + 8.85p2 = 0.00 0.002015 + -1p + 8.85p2 = 0.00 Begin completing the square. Divide all terms by 8.85 the coefficient of the squared term: Divide each side by '8.85'. 0.0002276836158 + -0.1129943503p + p2 = 0 Move the constant term to the right: Add '-0.0002276836158' to each side of the equation. 0.0002276836158 + -0.1129943503p + -0.0002276836158 + p2 = 0 + -0.0002276836158 Reorder the terms: 0.0002276836158 + -0.0002276836158 + -0.1129943503p + p2 = 0 + -0.0002276836158 Combine like terms: 0.0002276836158 + -0.0002276836158 = 0.0000000000000 0.0000000000000 + -0.1129943503p + p2 = 0 + -0.0002276836158 -0.1129943503p + p2 = 0 + -0.0002276836158 Combine like terms: 0 + -0.0002276836158 = -0.0002276836158 -0.1129943503p + p2 = -0.0002276836158 The p term is -0.1129943503p. Take half its coefficient (-0.05649717515). Square it (0.003191930800) and add it to both sides. Add '0.003191930800' to each side of the equation. -0.1129943503p + 0.003191930800 + p2 = -0.0002276836158 + 0.003191930800 Reorder the terms: 0.003191930800 + -0.1129943503p + p2 = -0.0002276836158 + 0.003191930800 Combine like terms: -0.0002276836158 + 0.003191930800 = 0.0029642471842 0.003191930800 + -0.1129943503p + p2 = 0.0029642471842 Factor a perfect square on the left side: (p + -0.05649717515)(p + -0.05649717515) = 0.0029642471842 Calculate the square root of the right side: 0.0544449 Break this problem into two subproblems by setting (p + -0.05649717515) equal to 0.0544449 and -0.0544449.Subproblem 1
p + -0.05649717515 = 0.0544449 Simplifying p + -0.05649717515 = 0.0544449 Reorder the terms: -0.05649717515 + p = 0.0544449 Solving -0.05649717515 + p = 0.0544449 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.05649717515' to each side of the equation. -0.05649717515 + 0.05649717515 + p = 0.0544449 + 0.05649717515 Combine like terms: -0.05649717515 + 0.05649717515 = 0.00000000000 0.00000000000 + p = 0.0544449 + 0.05649717515 p = 0.0544449 + 0.05649717515 Combine like terms: 0.0544449 + 0.05649717515 = 0.11094207515 p = 0.11094207515 Simplifying p = 0.11094207515Subproblem 2
p + -0.05649717515 = -0.0544449 Simplifying p + -0.05649717515 = -0.0544449 Reorder the terms: -0.05649717515 + p = -0.0544449 Solving -0.05649717515 + p = -0.0544449 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.05649717515' to each side of the equation. -0.05649717515 + 0.05649717515 + p = -0.0544449 + 0.05649717515 Combine like terms: -0.05649717515 + 0.05649717515 = 0.00000000000 0.00000000000 + p = -0.0544449 + 0.05649717515 p = -0.0544449 + 0.05649717515 Combine like terms: -0.0544449 + 0.05649717515 = 0.00205227515 p = 0.00205227515 Simplifying p = 0.00205227515Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.11094207515, 0.00205227515}
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