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Simplifying 9p2 = 2p + 20 Reorder the terms: 9p2 = 20 + 2p Solving 9p2 = 20 + 2p Solving for variable 'p'. Reorder the terms: -20 + -2p + 9p2 = 20 + 2p + -20 + -2p Reorder the terms: -20 + -2p + 9p2 = 20 + -20 + 2p + -2p Combine like terms: 20 + -20 = 0 -20 + -2p + 9p2 = 0 + 2p + -2p -20 + -2p + 9p2 = 2p + -2p Combine like terms: 2p + -2p = 0 -20 + -2p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + -0.2222222222p + p2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -0.2222222222p + 2.222222222 + p2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -0.2222222222p + p2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -0.2222222222p + p2 = 0 + 2.222222222 -0.2222222222p + p2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -0.2222222222p + p2 = 2.222222222 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 = 2.222222222 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222p + p2 = 2.222222222 + 0.01234567901 Combine like terms: 2.222222222 + 0.01234567901 = 2.23456790101 0.01234567901 + -0.2222222222p + p2 = 2.23456790101 Factor a perfect square on the left side: (p + -0.1111111111)(p + -0.1111111111) = 2.23456790101 Calculate the square root of the right side: 1.494847116 Break this problem into two subproblems by setting (p + -0.1111111111) equal to 1.494847116 and -1.494847116.Subproblem 1
p + -0.1111111111 = 1.494847116 Simplifying p + -0.1111111111 = 1.494847116 Reorder the terms: -0.1111111111 + p = 1.494847116 Solving -0.1111111111 + p = 1.494847116 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 = 1.494847116 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + p = 1.494847116 + 0.1111111111 p = 1.494847116 + 0.1111111111 Combine like terms: 1.494847116 + 0.1111111111 = 1.6059582271 p = 1.6059582271 Simplifying p = 1.6059582271Subproblem 2
p + -0.1111111111 = -1.494847116 Simplifying p + -0.1111111111 = -1.494847116 Reorder the terms: -0.1111111111 + p = -1.494847116 Solving -0.1111111111 + p = -1.494847116 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 = -1.494847116 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + p = -1.494847116 + 0.1111111111 p = -1.494847116 + 0.1111111111 Combine like terms: -1.494847116 + 0.1111111111 = -1.3837360049 p = -1.3837360049 Simplifying p = -1.3837360049Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.6059582271, -1.3837360049}
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