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Simplifying 2p2 + 1p + -4 = 0 Reorder the terms: -4 + 1p + 2p2 = 0 Solving -4 + 1p + 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 + 0.5p + p2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.5p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + 0.5p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.5p + p2 = 0 + 2 0.5p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.5p + p2 = 2 The p term is 0.5p. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5p + 0.0625 + p2 = 2 + 0.0625 Reorder the terms: 0.0625 + 0.5p + p2 = 2 + 0.0625 Combine like terms: 2 + 0.0625 = 2.0625 0.0625 + 0.5p + p2 = 2.0625 Factor a perfect square on the left side: (p + 0.25)(p + 0.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (p + 0.25) equal to 1.436140662 and -1.436140662.Subproblem 1
p + 0.25 = 1.436140662 Simplifying p + 0.25 = 1.436140662 Reorder the terms: 0.25 + p = 1.436140662 Solving 0.25 + p = 1.436140662 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + p = 1.436140662 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + p = 1.436140662 + -0.25 p = 1.436140662 + -0.25 Combine like terms: 1.436140662 + -0.25 = 1.186140662 p = 1.186140662 Simplifying p = 1.186140662Subproblem 2
p + 0.25 = -1.436140662 Simplifying p + 0.25 = -1.436140662 Reorder the terms: 0.25 + p = -1.436140662 Solving 0.25 + p = -1.436140662 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + p = -1.436140662 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + p = -1.436140662 + -0.25 p = -1.436140662 + -0.25 Combine like terms: -1.436140662 + -0.25 = -1.686140662 p = -1.686140662 Simplifying p = -1.686140662Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.186140662, -1.686140662}
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