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Simplifying 3p2 + -30p + -11 = 6 Reorder the terms: -11 + -30p + 3p2 = 6 Solving -11 + -30p + 3p2 = 6 Solving for variable 'p'. Reorder the terms: -11 + -6 + -30p + 3p2 = 6 + -6 Combine like terms: -11 + -6 = -17 -17 + -30p + 3p2 = 6 + -6 Combine like terms: 6 + -6 = 0 -17 + -30p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.666666667 + -10p + p2 = 0 Move the constant term to the right: Add '5.666666667' to each side of the equation. -5.666666667 + -10p + 5.666666667 + p2 = 0 + 5.666666667 Reorder the terms: -5.666666667 + 5.666666667 + -10p + p2 = 0 + 5.666666667 Combine like terms: -5.666666667 + 5.666666667 = 0.000000000 0.000000000 + -10p + p2 = 0 + 5.666666667 -10p + p2 = 0 + 5.666666667 Combine like terms: 0 + 5.666666667 = 5.666666667 -10p + p2 = 5.666666667 The p term is -10p. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10p + 25 + p2 = 5.666666667 + 25 Reorder the terms: 25 + -10p + p2 = 5.666666667 + 25 Combine like terms: 5.666666667 + 25 = 30.666666667 25 + -10p + p2 = 30.666666667 Factor a perfect square on the left side: (p + -5)(p + -5) = 30.666666667 Calculate the square root of the right side: 5.537749242 Break this problem into two subproblems by setting (p + -5) equal to 5.537749242 and -5.537749242.Subproblem 1
p + -5 = 5.537749242 Simplifying p + -5 = 5.537749242 Reorder the terms: -5 + p = 5.537749242 Solving -5 + p = 5.537749242 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = 5.537749242 + 5 Combine like terms: -5 + 5 = 0 0 + p = 5.537749242 + 5 p = 5.537749242 + 5 Combine like terms: 5.537749242 + 5 = 10.537749242 p = 10.537749242 Simplifying p = 10.537749242Subproblem 2
p + -5 = -5.537749242 Simplifying p + -5 = -5.537749242 Reorder the terms: -5 + p = -5.537749242 Solving -5 + p = -5.537749242 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = -5.537749242 + 5 Combine like terms: -5 + 5 = 0 0 + p = -5.537749242 + 5 p = -5.537749242 + 5 Combine like terms: -5.537749242 + 5 = -0.537749242 p = -0.537749242 Simplifying p = -0.537749242Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.537749242, -0.537749242}
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