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Simplifying -9p2 + 2p + 8 = 0 Reorder the terms: 8 + 2p + -9p2 = 0 Solving 8 + 2p + -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'. -0.8888888889 + -0.2222222222p + p2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.2222222222p + 0.8888888889 + p2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.2222222222p + p2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.2222222222p + p2 = 0 + 0.8888888889 -0.2222222222p + p2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.2222222222p + p2 = 0.8888888889 The p term is -0.2222222222p. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222p + 0.01234567901 + p2 = 0.8888888889 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222p + p2 = 0.8888888889 + 0.01234567901 Combine like terms: 0.8888888889 + 0.01234567901 = 0.90123456791 0.01234567901 + -0.2222222222p + p2 = 0.90123456791 Factor a perfect square on the left side: (p + -0.1111111111)(p + -0.1111111111) = 0.90123456791 Calculate the square root of the right side: 0.949333749 Break this problem into two subproblems by setting (p + -0.1111111111) equal to 0.949333749 and -0.949333749.Subproblem 1
p + -0.1111111111 = 0.949333749 Simplifying p + -0.1111111111 = 0.949333749 Reorder the terms: -0.1111111111 + p = 0.949333749 Solving -0.1111111111 + p = 0.949333749 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + p = 0.949333749 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + p = 0.949333749 + 0.1111111111 p = 0.949333749 + 0.1111111111 Combine like terms: 0.949333749 + 0.1111111111 = 1.0604448601 p = 1.0604448601 Simplifying p = 1.0604448601Subproblem 2
p + -0.1111111111 = -0.949333749 Simplifying p + -0.1111111111 = -0.949333749 Reorder the terms: -0.1111111111 + p = -0.949333749 Solving -0.1111111111 + p = -0.949333749 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + p = -0.949333749 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + p = -0.949333749 + 0.1111111111 p = -0.949333749 + 0.1111111111 Combine like terms: -0.949333749 + 0.1111111111 = -0.8382226379 p = -0.8382226379 Simplifying p = -0.8382226379Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.0604448601, -0.8382226379}
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