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Simplifying 0 = 5p2 + -12p + -16 Reorder the terms: 0 = -16 + -12p + 5p2 Solving 0 = -16 + -12p + 5p2 Solving for variable 'p'. Combine like terms: 0 + 16 = 16 16 + 12p + -5p2 = -16 + -12p + 5p2 + 16 + 12p + -5p2 Reorder the terms: 16 + 12p + -5p2 = -16 + 16 + -12p + 12p + 5p2 + -5p2 Combine like terms: -16 + 16 = 0 16 + 12p + -5p2 = 0 + -12p + 12p + 5p2 + -5p2 16 + 12p + -5p2 = -12p + 12p + 5p2 + -5p2 Combine like terms: -12p + 12p = 0 16 + 12p + -5p2 = 0 + 5p2 + -5p2 16 + 12p + -5p2 = 5p2 + -5p2 Combine like terms: 5p2 + -5p2 = 0 16 + 12p + -5p2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.2 + -2.4p + p2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -2.4p + 3.2 + p2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -2.4p + p2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -2.4p + p2 = 0 + 3.2 -2.4p + p2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -2.4p + p2 = 3.2 The p term is -2.4p. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4p + 1.44 + p2 = 3.2 + 1.44 Reorder the terms: 1.44 + -2.4p + p2 = 3.2 + 1.44 Combine like terms: 3.2 + 1.44 = 4.64 1.44 + -2.4p + p2 = 4.64 Factor a perfect square on the left side: (p + -1.2)(p + -1.2) = 4.64 Calculate the square root of the right side: 2.154065923 Break this problem into two subproblems by setting (p + -1.2) equal to 2.154065923 and -2.154065923.Subproblem 1
p + -1.2 = 2.154065923 Simplifying p + -1.2 = 2.154065923 Reorder the terms: -1.2 + p = 2.154065923 Solving -1.2 + p = 2.154065923 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + p = 2.154065923 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + p = 2.154065923 + 1.2 p = 2.154065923 + 1.2 Combine like terms: 2.154065923 + 1.2 = 3.354065923 p = 3.354065923 Simplifying p = 3.354065923Subproblem 2
p + -1.2 = -2.154065923 Simplifying p + -1.2 = -2.154065923 Reorder the terms: -1.2 + p = -2.154065923 Solving -1.2 + p = -2.154065923 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + p = -2.154065923 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + p = -2.154065923 + 1.2 p = -2.154065923 + 1.2 Combine like terms: -2.154065923 + 1.2 = -0.954065923 p = -0.954065923 Simplifying p = -0.954065923Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.354065923, -0.954065923}
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