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Simplifying 4p2 + -9 = -1p Reorder the terms: -9 + 4p2 = -1p Solving -9 + 4p2 = -1p Solving for variable 'p'. Reorder the terms: -9 + p + 4p2 = -1p + p Combine like terms: -1p + p = 0 -9 + p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 0.25p + p2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 0.25p + 2.25 + p2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 0.25p + p2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 0.25p + p2 = 0 + 2.25 0.25p + p2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 0.25p + p2 = 2.25 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25p + 0.25 + p2 = 2.25 + 0.25 Reorder the terms: 0.25 + 0.25p + p2 = 2.25 + 0.25 Combine like terms: 2.25 + 0.25 = 2.5 0.25 + 0.25p + p2 = 2.5 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (p + 0.5) equal to 1.58113883 and -1.58113883.Subproblem 1
p + 0.5 = 1.58113883 Simplifying p + 0.5 = 1.58113883 Reorder the terms: 0.5 + p = 1.58113883 Solving 0.5 + p = 1.58113883 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 1.58113883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 1.58113883 + -0.5 p = 1.58113883 + -0.5 Combine like terms: 1.58113883 + -0.5 = 1.08113883 p = 1.08113883 Simplifying p = 1.08113883Subproblem 2
p + 0.5 = -1.58113883 Simplifying p + 0.5 = -1.58113883 Reorder the terms: 0.5 + p = -1.58113883 Solving 0.5 + p = -1.58113883 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -1.58113883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -1.58113883 + -0.5 p = -1.58113883 + -0.5 Combine like terms: -1.58113883 + -0.5 = -2.08113883 p = -2.08113883 Simplifying p = -2.08113883Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.08113883, -2.08113883}
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