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Simplifying 3p2 + -30 + -11 = 6p Reorder the terms: -30 + -11 + 3p2 = 6p Combine like terms: -30 + -11 = -41 -41 + 3p2 = 6p Solving -41 + 3p2 = 6p Solving for variable 'p'. Reorder the terms: -41 + -6p + 3p2 = 6p + -6p Combine like terms: 6p + -6p = 0 -41 + -6p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.66666667 + -2p + p2 = 0 Move the constant term to the right: Add '13.66666667' to each side of the equation. -13.66666667 + -2p + 13.66666667 + p2 = 0 + 13.66666667 Reorder the terms: -13.66666667 + 13.66666667 + -2p + p2 = 0 + 13.66666667 Combine like terms: -13.66666667 + 13.66666667 = 0.00000000 0.00000000 + -2p + p2 = 0 + 13.66666667 -2p + p2 = 0 + 13.66666667 Combine like terms: 0 + 13.66666667 = 13.66666667 -2p + p2 = 13.66666667 The p term is -2p. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2p + 1 + p2 = 13.66666667 + 1 Reorder the terms: 1 + -2p + p2 = 13.66666667 + 1 Combine like terms: 13.66666667 + 1 = 14.66666667 1 + -2p + p2 = 14.66666667 Factor a perfect square on the left side: (p + -1)(p + -1) = 14.66666667 Calculate the square root of the right side: 3.829708431 Break this problem into two subproblems by setting (p + -1) equal to 3.829708431 and -3.829708431.Subproblem 1
p + -1 = 3.829708431 Simplifying p + -1 = 3.829708431 Reorder the terms: -1 + p = 3.829708431 Solving -1 + p = 3.829708431 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = 3.829708431 + 1 Combine like terms: -1 + 1 = 0 0 + p = 3.829708431 + 1 p = 3.829708431 + 1 Combine like terms: 3.829708431 + 1 = 4.829708431 p = 4.829708431 Simplifying p = 4.829708431Subproblem 2
p + -1 = -3.829708431 Simplifying p + -1 = -3.829708431 Reorder the terms: -1 + p = -3.829708431 Solving -1 + p = -3.829708431 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = -3.829708431 + 1 Combine like terms: -1 + 1 = 0 0 + p = -3.829708431 + 1 p = -3.829708431 + 1 Combine like terms: -3.829708431 + 1 = -2.829708431 p = -2.829708431 Simplifying p = -2.829708431Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.829708431, -2.829708431}
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