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Simplifying 4p2 + 16p = 15 Reorder the terms: 16p + 4p2 = 15 Solving 16p + 4p2 = 15 Solving for variable 'p'. Reorder the terms: -15 + 16p + 4p2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 16p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 4p + p2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 4p + 3.75 + p2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 4p + p2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 4p + p2 = 0 + 3.75 4p + p2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 4p + p2 = 3.75 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 3.75 + 4 Reorder the terms: 4 + 4p + p2 = 3.75 + 4 Combine like terms: 3.75 + 4 = 7.75 4 + 4p + p2 = 7.75 Factor a perfect square on the left side: (p + 2)(p + 2) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (p + 2) equal to 2.783882181 and -2.783882181.Subproblem 1
p + 2 = 2.783882181 Simplifying p + 2 = 2.783882181 Reorder the terms: 2 + p = 2.783882181 Solving 2 + p = 2.783882181 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 2.783882181 + -2 Combine like terms: 2 + -2 = 0 0 + p = 2.783882181 + -2 p = 2.783882181 + -2 Combine like terms: 2.783882181 + -2 = 0.783882181 p = 0.783882181 Simplifying p = 0.783882181Subproblem 2
p + 2 = -2.783882181 Simplifying p + 2 = -2.783882181 Reorder the terms: 2 + p = -2.783882181 Solving 2 + p = -2.783882181 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -2.783882181 + -2 Combine like terms: 2 + -2 = 0 0 + p = -2.783882181 + -2 p = -2.783882181 + -2 Combine like terms: -2.783882181 + -2 = -4.783882181 p = -4.783882181 Simplifying p = -4.783882181Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.783882181, -4.783882181}
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