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Simplifying (7p2 + -6p + -1) + -1(-8p2 + 3p + 3) = 0 Reorder the terms: (-1 + -6p + 7p2) + -1(-8p2 + 3p + 3) = 0 Remove parenthesis around (-1 + -6p + 7p2) -1 + -6p + 7p2 + -1(-8p2 + 3p + 3) = 0 Reorder the terms: -1 + -6p + 7p2 + -1(3 + 3p + -8p2) = 0 -1 + -6p + 7p2 + (3 * -1 + 3p * -1 + -8p2 * -1) = 0 -1 + -6p + 7p2 + (-3 + -3p + 8p2) = 0 Reorder the terms: -1 + -3 + -6p + -3p + 7p2 + 8p2 = 0 Combine like terms: -1 + -3 = -4 -4 + -6p + -3p + 7p2 + 8p2 = 0 Combine like terms: -6p + -3p = -9p -4 + -9p + 7p2 + 8p2 = 0 Combine like terms: 7p2 + 8p2 = 15p2 -4 + -9p + 15p2 = 0 Solving -4 + -9p + 15p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2666666667 + -0.6p + p2 = 0 Move the constant term to the right: Add '0.2666666667' to each side of the equation. -0.2666666667 + -0.6p + 0.2666666667 + p2 = 0 + 0.2666666667 Reorder the terms: -0.2666666667 + 0.2666666667 + -0.6p + p2 = 0 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + -0.6p + p2 = 0 + 0.2666666667 -0.6p + p2 = 0 + 0.2666666667 Combine like terms: 0 + 0.2666666667 = 0.2666666667 -0.6p + p2 = 0.2666666667 The p term is -0.6p. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6p + 0.09 + p2 = 0.2666666667 + 0.09 Reorder the terms: 0.09 + -0.6p + p2 = 0.2666666667 + 0.09 Combine like terms: 0.2666666667 + 0.09 = 0.3566666667 0.09 + -0.6p + p2 = 0.3566666667 Factor a perfect square on the left side: (p + -0.3)(p + -0.3) = 0.3566666667 Calculate the square root of the right side: 0.597215762 Break this problem into two subproblems by setting (p + -0.3) equal to 0.597215762 and -0.597215762.Subproblem 1
p + -0.3 = 0.597215762 Simplifying p + -0.3 = 0.597215762 Reorder the terms: -0.3 + p = 0.597215762 Solving -0.3 + p = 0.597215762 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + p = 0.597215762 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + p = 0.597215762 + 0.3 p = 0.597215762 + 0.3 Combine like terms: 0.597215762 + 0.3 = 0.897215762 p = 0.897215762 Simplifying p = 0.897215762Subproblem 2
p + -0.3 = -0.597215762 Simplifying p + -0.3 = -0.597215762 Reorder the terms: -0.3 + p = -0.597215762 Solving -0.3 + p = -0.597215762 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + p = -0.597215762 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + p = -0.597215762 + 0.3 p = -0.597215762 + 0.3 Combine like terms: -0.597215762 + 0.3 = -0.297215762 p = -0.297215762 Simplifying p = -0.297215762Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.897215762, -0.297215762}
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