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Simplifying 9p2 + -30p = 16 Reorder the terms: -30p + 9p2 = 16 Solving -30p + 9p2 = 16 Solving for variable 'p'. Reorder the terms: -16 + -30p + 9p2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -30p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + -3.333333333p + p2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -3.333333333p + 1.777777778 + p2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -3.333333333p + p2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -3.333333333p + p2 = 0 + 1.777777778 -3.333333333p + p2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -3.333333333p + p2 = 1.777777778 The p term is -3.333333333p. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333p + 2.777777779 + p2 = 1.777777778 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333p + p2 = 1.777777778 + 2.777777779 Combine like terms: 1.777777778 + 2.777777779 = 4.555555557 2.777777779 + -3.333333333p + p2 = 4.555555557 Factor a perfect square on the left side: (p + -1.666666667)(p + -1.666666667) = 4.555555557 Calculate the square root of the right side: 2.134374746 Break this problem into two subproblems by setting (p + -1.666666667) equal to 2.134374746 and -2.134374746.Subproblem 1
p + -1.666666667 = 2.134374746 Simplifying p + -1.666666667 = 2.134374746 Reorder the terms: -1.666666667 + p = 2.134374746 Solving -1.666666667 + p = 2.134374746 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + p = 2.134374746 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + p = 2.134374746 + 1.666666667 p = 2.134374746 + 1.666666667 Combine like terms: 2.134374746 + 1.666666667 = 3.801041413 p = 3.801041413 Simplifying p = 3.801041413Subproblem 2
p + -1.666666667 = -2.134374746 Simplifying p + -1.666666667 = -2.134374746 Reorder the terms: -1.666666667 + p = -2.134374746 Solving -1.666666667 + p = -2.134374746 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + p = -2.134374746 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + p = -2.134374746 + 1.666666667 p = -2.134374746 + 1.666666667 Combine like terms: -2.134374746 + 1.666666667 = -0.467708079 p = -0.467708079 Simplifying p = -0.467708079Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.801041413, -0.467708079}
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