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Simplifying 9p2 + 8p + -3 = 0 Reorder the terms: -3 + 8p + 9p2 = 0 Solving -3 + 8p + 9p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.3333333333 + 0.8888888889p + p2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.8888888889p + 0.3333333333 + p2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.8888888889p + p2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.8888888889p + p2 = 0 + 0.3333333333 0.8888888889p + p2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.8888888889p + p2 = 0.3333333333 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 = 0.3333333333 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889p + p2 = 0.3333333333 + 0.1975308642 Combine like terms: 0.3333333333 + 0.1975308642 = 0.5308641975 0.1975308642 + 0.8888888889p + p2 = 0.5308641975 Factor a perfect square on the left side: (p + 0.4444444445)(p + 0.4444444445) = 0.5308641975 Calculate the square root of the right side: 0.72860428 Break this problem into two subproblems by setting (p + 0.4444444445) equal to 0.72860428 and -0.72860428.Subproblem 1
p + 0.4444444445 = 0.72860428 Simplifying p + 0.4444444445 = 0.72860428 Reorder the terms: 0.4444444445 + p = 0.72860428 Solving 0.4444444445 + p = 0.72860428 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 = 0.72860428 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + p = 0.72860428 + -0.4444444445 p = 0.72860428 + -0.4444444445 Combine like terms: 0.72860428 + -0.4444444445 = 0.2841598355 p = 0.2841598355 Simplifying p = 0.2841598355Subproblem 2
p + 0.4444444445 = -0.72860428 Simplifying p + 0.4444444445 = -0.72860428 Reorder the terms: 0.4444444445 + p = -0.72860428 Solving 0.4444444445 + p = -0.72860428 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 = -0.72860428 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + p = -0.72860428 + -0.4444444445 p = -0.72860428 + -0.4444444445 Combine like terms: -0.72860428 + -0.4444444445 = -1.1730487245 p = -1.1730487245 Simplifying p = -1.1730487245Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.2841598355, -1.1730487245}
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