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Simplifying 2p2 + 18p + 5 = 0 Reorder the terms: 5 + 18p + 2p2 = 0 Solving 5 + 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'. 2.5 + 9p + p2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 9p + -2.5 + p2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 9p + p2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 9p + p2 = 0 + -2.5 9p + p2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 9p + p2 = -2.5 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 = -2.5 + 20.25 Reorder the terms: 20.25 + 9p + p2 = -2.5 + 20.25 Combine like terms: -2.5 + 20.25 = 17.75 20.25 + 9p + p2 = 17.75 Factor a perfect square on the left side: (p + 4.5)(p + 4.5) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (p + 4.5) equal to 4.213074887 and -4.213074887.Subproblem 1
p + 4.5 = 4.213074887 Simplifying p + 4.5 = 4.213074887 Reorder the terms: 4.5 + p = 4.213074887 Solving 4.5 + p = 4.213074887 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 = 4.213074887 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = 4.213074887 + -4.5 p = 4.213074887 + -4.5 Combine like terms: 4.213074887 + -4.5 = -0.286925113 p = -0.286925113 Simplifying p = -0.286925113Subproblem 2
p + 4.5 = -4.213074887 Simplifying p + 4.5 = -4.213074887 Reorder the terms: 4.5 + p = -4.213074887 Solving 4.5 + p = -4.213074887 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 = -4.213074887 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = -4.213074887 + -4.5 p = -4.213074887 + -4.5 Combine like terms: -4.213074887 + -4.5 = -8.713074887 p = -8.713074887 Simplifying p = -8.713074887Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.286925113, -8.713074887}
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