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Simplifying 2p2 + 33p + 42 = 0 Reorder the terms: 42 + 33p + 2p2 = 0 Solving 42 + 33p + 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'. 21 + 16.5p + p2 = 0 Move the constant term to the right: Add '-21' to each side of the equation. 21 + 16.5p + -21 + p2 = 0 + -21 Reorder the terms: 21 + -21 + 16.5p + p2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 16.5p + p2 = 0 + -21 16.5p + p2 = 0 + -21 Combine like terms: 0 + -21 = -21 16.5p + p2 = -21 The p term is 16.5p. Take half its coefficient (8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. 16.5p + 68.0625 + p2 = -21 + 68.0625 Reorder the terms: 68.0625 + 16.5p + p2 = -21 + 68.0625 Combine like terms: -21 + 68.0625 = 47.0625 68.0625 + 16.5p + p2 = 47.0625 Factor a perfect square on the left side: (p + 8.25)(p + 8.25) = 47.0625 Calculate the square root of the right side: 6.860211367 Break this problem into two subproblems by setting (p + 8.25) equal to 6.860211367 and -6.860211367.Subproblem 1
p + 8.25 = 6.860211367 Simplifying p + 8.25 = 6.860211367 Reorder the terms: 8.25 + p = 6.860211367 Solving 8.25 + p = 6.860211367 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + p = 6.860211367 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + p = 6.860211367 + -8.25 p = 6.860211367 + -8.25 Combine like terms: 6.860211367 + -8.25 = -1.389788633 p = -1.389788633 Simplifying p = -1.389788633Subproblem 2
p + 8.25 = -6.860211367 Simplifying p + 8.25 = -6.860211367 Reorder the terms: 8.25 + p = -6.860211367 Solving 8.25 + p = -6.860211367 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + p = -6.860211367 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + p = -6.860211367 + -8.25 p = -6.860211367 + -8.25 Combine like terms: -6.860211367 + -8.25 = -15.110211367 p = -15.110211367 Simplifying p = -15.110211367Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.389788633, -15.110211367}
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