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Simplifying 9p2 + -6 = -8p Reorder the terms: -6 + 9p2 = -8p Solving -6 + 9p2 = -8p Solving for variable 'p'. Reorder the terms: -6 + 8p + 9p2 = -8p + 8p Combine like terms: -8p + 8p = 0 -6 + 8p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.6666666667 + 0.8888888889p + p2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.8888888889p + 0.6666666667 + p2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.8888888889p + p2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.8888888889p + p2 = 0 + 0.6666666667 0.8888888889p + p2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.8888888889p + p2 = 0.6666666667 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 = 0.6666666667 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889p + p2 = 0.6666666667 + 0.1975308642 Combine like terms: 0.6666666667 + 0.1975308642 = 0.8641975309 0.1975308642 + 0.8888888889p + p2 = 0.8641975309 Factor a perfect square on the left side: (p + 0.4444444445)(p + 0.4444444445) = 0.8641975309 Calculate the square root of the right side: 0.929622252 Break this problem into two subproblems by setting (p + 0.4444444445) equal to 0.929622252 and -0.929622252.Subproblem 1
p + 0.4444444445 = 0.929622252 Simplifying p + 0.4444444445 = 0.929622252 Reorder the terms: 0.4444444445 + p = 0.929622252 Solving 0.4444444445 + p = 0.929622252 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 = 0.929622252 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + p = 0.929622252 + -0.4444444445 p = 0.929622252 + -0.4444444445 Combine like terms: 0.929622252 + -0.4444444445 = 0.4851778075 p = 0.4851778075 Simplifying p = 0.4851778075Subproblem 2
p + 0.4444444445 = -0.929622252 Simplifying p + 0.4444444445 = -0.929622252 Reorder the terms: 0.4444444445 + p = -0.929622252 Solving 0.4444444445 + p = -0.929622252 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 = -0.929622252 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + p = -0.929622252 + -0.4444444445 p = -0.929622252 + -0.4444444445 Combine like terms: -0.929622252 + -0.4444444445 = -1.3740666965 p = -1.3740666965 Simplifying p = -1.3740666965Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.4851778075, -1.3740666965}
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