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Simplifying (p + 27) + p(4p + -37) = 644 Reorder the terms: (27 + p) + p(4p + -37) = 644 Remove parenthesis around (27 + p) 27 + p + p(4p + -37) = 644 Reorder the terms: 27 + p + p(-37 + 4p) = 644 27 + p + (-37 * p + 4p * p) = 644 27 + p + (-37p + 4p2) = 644 Combine like terms: p + -37p = -36p 27 + -36p + 4p2 = 644 Solving 27 + -36p + 4p2 = 644 Solving for variable 'p'. Reorder the terms: 27 + -644 + -36p + 4p2 = 644 + -644 Combine like terms: 27 + -644 = -617 -617 + -36p + 4p2 = 644 + -644 Combine like terms: 644 + -644 = 0 -617 + -36p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -154.25 + -9p + p2 = 0 Move the constant term to the right: Add '154.25' to each side of the equation. -154.25 + -9p + 154.25 + p2 = 0 + 154.25 Reorder the terms: -154.25 + 154.25 + -9p + p2 = 0 + 154.25 Combine like terms: -154.25 + 154.25 = 0.00 0.00 + -9p + p2 = 0 + 154.25 -9p + p2 = 0 + 154.25 Combine like terms: 0 + 154.25 = 154.25 -9p + p2 = 154.25 The p term is -9p. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9p + 20.25 + p2 = 154.25 + 20.25 Reorder the terms: 20.25 + -9p + p2 = 154.25 + 20.25 Combine like terms: 154.25 + 20.25 = 174.5 20.25 + -9p + p2 = 174.5 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 174.5 Calculate the square root of the right side: 13.209844814 Break this problem into two subproblems by setting (p + -4.5) equal to 13.209844814 and -13.209844814.Subproblem 1
p + -4.5 = 13.209844814 Simplifying p + -4.5 = 13.209844814 Reorder the terms: -4.5 + p = 13.209844814 Solving -4.5 + p = 13.209844814 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = 13.209844814 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 13.209844814 + 4.5 p = 13.209844814 + 4.5 Combine like terms: 13.209844814 + 4.5 = 17.709844814 p = 17.709844814 Simplifying p = 17.709844814Subproblem 2
p + -4.5 = -13.209844814 Simplifying p + -4.5 = -13.209844814 Reorder the terms: -4.5 + p = -13.209844814 Solving -4.5 + p = -13.209844814 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = -13.209844814 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -13.209844814 + 4.5 p = -13.209844814 + 4.5 Combine like terms: -13.209844814 + 4.5 = -8.709844814 p = -8.709844814 Simplifying p = -8.709844814Solution
The solution to the problem is based on the solutions from the subproblems. p = {17.709844814, -8.709844814}
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