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Simplifying 3p2 + -18p + 13 = 0 Reorder the terms: 13 + -18p + 3p2 = 0 Solving 13 + -18p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.333333333 + -6p + p2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + -6p + -4.333333333 + p2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + -6p + p2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + -6p + p2 = 0 + -4.333333333 -6p + p2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 -6p + p2 = -4.333333333 The p term is -6p. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6p + 9 + p2 = -4.333333333 + 9 Reorder the terms: 9 + -6p + p2 = -4.333333333 + 9 Combine like terms: -4.333333333 + 9 = 4.666666667 9 + -6p + p2 = 4.666666667 Factor a perfect square on the left side: (p + -3)(p + -3) = 4.666666667 Calculate the square root of the right side: 2.1602469 Break this problem into two subproblems by setting (p + -3) equal to 2.1602469 and -2.1602469.Subproblem 1
p + -3 = 2.1602469 Simplifying p + -3 = 2.1602469 Reorder the terms: -3 + p = 2.1602469 Solving -3 + p = 2.1602469 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = 2.1602469 + 3 Combine like terms: -3 + 3 = 0 0 + p = 2.1602469 + 3 p = 2.1602469 + 3 Combine like terms: 2.1602469 + 3 = 5.1602469 p = 5.1602469 Simplifying p = 5.1602469Subproblem 2
p + -3 = -2.1602469 Simplifying p + -3 = -2.1602469 Reorder the terms: -3 + p = -2.1602469 Solving -3 + p = -2.1602469 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = -2.1602469 + 3 Combine like terms: -3 + 3 = 0 0 + p = -2.1602469 + 3 p = -2.1602469 + 3 Combine like terms: -2.1602469 + 3 = 0.8397531 p = 0.8397531 Simplifying p = 0.8397531Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.1602469, 0.8397531}
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