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Simplifying 2p2 + -18p + -11 = 0 Reorder the terms: -11 + -18p + 2p2 = 0 Solving -11 + -18p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -9p + p2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -9p + 5.5 + p2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -9p + p2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -9p + p2 = 0 + 5.5 -9p + p2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -9p + p2 = 5.5 The p term is -9p. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9p + 20.25 + p2 = 5.5 + 20.25 Reorder the terms: 20.25 + -9p + p2 = 5.5 + 20.25 Combine like terms: 5.5 + 20.25 = 25.75 20.25 + -9p + p2 = 25.75 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 25.75 Calculate the square root of the right side: 5.074445783 Break this problem into two subproblems by setting (p + -4.5) equal to 5.074445783 and -5.074445783.Subproblem 1
p + -4.5 = 5.074445783 Simplifying p + -4.5 = 5.074445783 Reorder the terms: -4.5 + p = 5.074445783 Solving -4.5 + p = 5.074445783 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = 5.074445783 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 5.074445783 + 4.5 p = 5.074445783 + 4.5 Combine like terms: 5.074445783 + 4.5 = 9.574445783 p = 9.574445783 Simplifying p = 9.574445783Subproblem 2
p + -4.5 = -5.074445783 Simplifying p + -4.5 = -5.074445783 Reorder the terms: -4.5 + p = -5.074445783 Solving -4.5 + p = -5.074445783 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = -5.074445783 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -5.074445783 + 4.5 p = -5.074445783 + 4.5 Combine like terms: -5.074445783 + 4.5 = -0.574445783 p = -0.574445783 Simplifying p = -0.574445783Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.574445783, -0.574445783}
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