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Simplifying 9p2 = 8p + 13 Reorder the terms: 9p2 = 13 + 8p Solving 9p2 = 13 + 8p Solving for variable 'p'. Reorder the terms: -13 + -8p + 9p2 = 13 + 8p + -13 + -8p Reorder the terms: -13 + -8p + 9p2 = 13 + -13 + 8p + -8p Combine like terms: 13 + -13 = 0 -13 + -8p + 9p2 = 0 + 8p + -8p -13 + -8p + 9p2 = 8p + -8p Combine like terms: 8p + -8p = 0 -13 + -8p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.444444444 + -0.8888888889p + p2 = 0 Move the constant term to the right: Add '1.444444444' to each side of the equation. -1.444444444 + -0.8888888889p + 1.444444444 + p2 = 0 + 1.444444444 Reorder the terms: -1.444444444 + 1.444444444 + -0.8888888889p + p2 = 0 + 1.444444444 Combine like terms: -1.444444444 + 1.444444444 = 0.000000000 0.000000000 + -0.8888888889p + p2 = 0 + 1.444444444 -0.8888888889p + p2 = 0 + 1.444444444 Combine like terms: 0 + 1.444444444 = 1.444444444 -0.8888888889p + p2 = 1.444444444 The p term is -0.8888888889p. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889p + 0.1975308642 + p2 = 1.444444444 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889p + p2 = 1.444444444 + 0.1975308642 Combine like terms: 1.444444444 + 0.1975308642 = 1.6419753082 0.1975308642 + -0.8888888889p + p2 = 1.6419753082 Factor a perfect square on the left side: (p + -0.4444444445)(p + -0.4444444445) = 1.6419753082 Calculate the square root of the right side: 1.281395844 Break this problem into two subproblems by setting (p + -0.4444444445) equal to 1.281395844 and -1.281395844.Subproblem 1
p + -0.4444444445 = 1.281395844 Simplifying p + -0.4444444445 = 1.281395844 Reorder the terms: -0.4444444445 + p = 1.281395844 Solving -0.4444444445 + p = 1.281395844 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + p = 1.281395844 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + p = 1.281395844 + 0.4444444445 p = 1.281395844 + 0.4444444445 Combine like terms: 1.281395844 + 0.4444444445 = 1.7258402885 p = 1.7258402885 Simplifying p = 1.7258402885Subproblem 2
p + -0.4444444445 = -1.281395844 Simplifying p + -0.4444444445 = -1.281395844 Reorder the terms: -0.4444444445 + p = -1.281395844 Solving -0.4444444445 + p = -1.281395844 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + p = -1.281395844 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + p = -1.281395844 + 0.4444444445 p = -1.281395844 + 0.4444444445 Combine like terms: -1.281395844 + 0.4444444445 = -0.8369513995 p = -0.8369513995 Simplifying p = -0.8369513995Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.7258402885, -0.8369513995}
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