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Simplifying (8p2 + -6p + -6) + -1(-5p2 + 2p + 8) = 0 Reorder the terms: (-6 + -6p + 8p2) + -1(-5p2 + 2p + 8) = 0 Remove parenthesis around (-6 + -6p + 8p2) -6 + -6p + 8p2 + -1(-5p2 + 2p + 8) = 0 Reorder the terms: -6 + -6p + 8p2 + -1(8 + 2p + -5p2) = 0 -6 + -6p + 8p2 + (8 * -1 + 2p * -1 + -5p2 * -1) = 0 -6 + -6p + 8p2 + (-8 + -2p + 5p2) = 0 Reorder the terms: -6 + -8 + -6p + -2p + 8p2 + 5p2 = 0 Combine like terms: -6 + -8 = -14 -14 + -6p + -2p + 8p2 + 5p2 = 0 Combine like terms: -6p + -2p = -8p -14 + -8p + 8p2 + 5p2 = 0 Combine like terms: 8p2 + 5p2 = 13p2 -14 + -8p + 13p2 = 0 Solving -14 + -8p + 13p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1.076923077 + -0.6153846154p + p2 = 0 Move the constant term to the right: Add '1.076923077' to each side of the equation. -1.076923077 + -0.6153846154p + 1.076923077 + p2 = 0 + 1.076923077 Reorder the terms: -1.076923077 + 1.076923077 + -0.6153846154p + p2 = 0 + 1.076923077 Combine like terms: -1.076923077 + 1.076923077 = 0.000000000 0.000000000 + -0.6153846154p + p2 = 0 + 1.076923077 -0.6153846154p + p2 = 0 + 1.076923077 Combine like terms: 0 + 1.076923077 = 1.076923077 -0.6153846154p + p2 = 1.076923077 The p term is -0.6153846154p. Take half its coefficient (-0.3076923077). Square it (0.09467455622) and add it to both sides. Add '0.09467455622' to each side of the equation. -0.6153846154p + 0.09467455622 + p2 = 1.076923077 + 0.09467455622 Reorder the terms: 0.09467455622 + -0.6153846154p + p2 = 1.076923077 + 0.09467455622 Combine like terms: 1.076923077 + 0.09467455622 = 1.17159763322 0.09467455622 + -0.6153846154p + p2 = 1.17159763322 Factor a perfect square on the left side: (p + -0.3076923077)(p + -0.3076923077) = 1.17159763322 Calculate the square root of the right side: 1.082403637 Break this problem into two subproblems by setting (p + -0.3076923077) equal to 1.082403637 and -1.082403637.Subproblem 1
p + -0.3076923077 = 1.082403637 Simplifying p + -0.3076923077 = 1.082403637 Reorder the terms: -0.3076923077 + p = 1.082403637 Solving -0.3076923077 + p = 1.082403637 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.3076923077 + p = 1.082403637 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + p = 1.082403637 + 0.3076923077 p = 1.082403637 + 0.3076923077 Combine like terms: 1.082403637 + 0.3076923077 = 1.3900959447 p = 1.3900959447 Simplifying p = 1.3900959447Subproblem 2
p + -0.3076923077 = -1.082403637 Simplifying p + -0.3076923077 = -1.082403637 Reorder the terms: -0.3076923077 + p = -1.082403637 Solving -0.3076923077 + p = -1.082403637 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.3076923077 + p = -1.082403637 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + p = -1.082403637 + 0.3076923077 p = -1.082403637 + 0.3076923077 Combine like terms: -1.082403637 + 0.3076923077 = -0.7747113293 p = -0.7747113293 Simplifying p = -0.7747113293Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.3900959447, -0.7747113293}
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