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Simplifying 4p2 + 21p + -64 = 0 Reorder the terms: -64 + 21p + 4p2 = 0 Solving -64 + 21p + 4p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -16 + 5.25p + p2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 5.25p + 16 + p2 = 0 + 16 Reorder the terms: -16 + 16 + 5.25p + p2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 5.25p + p2 = 0 + 16 5.25p + p2 = 0 + 16 Combine like terms: 0 + 16 = 16 5.25p + p2 = 16 The p term is 5.25p. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25p + 6.890625 + p2 = 16 + 6.890625 Reorder the terms: 6.890625 + 5.25p + p2 = 16 + 6.890625 Combine like terms: 16 + 6.890625 = 22.890625 6.890625 + 5.25p + p2 = 22.890625 Factor a perfect square on the left side: (p + 2.625)(p + 2.625) = 22.890625 Calculate the square root of the right side: 4.784414802 Break this problem into two subproblems by setting (p + 2.625) equal to 4.784414802 and -4.784414802.Subproblem 1
p + 2.625 = 4.784414802 Simplifying p + 2.625 = 4.784414802 Reorder the terms: 2.625 + p = 4.784414802 Solving 2.625 + p = 4.784414802 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + p = 4.784414802 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + p = 4.784414802 + -2.625 p = 4.784414802 + -2.625 Combine like terms: 4.784414802 + -2.625 = 2.159414802 p = 2.159414802 Simplifying p = 2.159414802Subproblem 2
p + 2.625 = -4.784414802 Simplifying p + 2.625 = -4.784414802 Reorder the terms: 2.625 + p = -4.784414802 Solving 2.625 + p = -4.784414802 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + p = -4.784414802 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + p = -4.784414802 + -2.625 p = -4.784414802 + -2.625 Combine like terms: -4.784414802 + -2.625 = -7.409414802 p = -7.409414802 Simplifying p = -7.409414802Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.159414802, -7.409414802}
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