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Simplifying 9p2 + 6p + -17 = 0 Reorder the terms: -17 + 6p + 9p2 = 0 Solving -17 + 6p + 9p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.888888889 + 0.6666666667p + p2 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + 0.6666666667p + 1.888888889 + p2 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + 0.6666666667p + p2 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + 0.6666666667p + p2 = 0 + 1.888888889 0.6666666667p + p2 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 0.6666666667p + p2 = 1.888888889 The p term is 0.6666666667p. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667p + 0.1111111112 + p2 = 1.888888889 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667p + p2 = 1.888888889 + 0.1111111112 Combine like terms: 1.888888889 + 0.1111111112 = 2.0000000002 0.1111111112 + 0.6666666667p + p2 = 2.0000000002 Factor a perfect square on the left side: (p + 0.3333333334)(p + 0.3333333334) = 2.0000000002 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (p + 0.3333333334) equal to 1.414213562 and -1.414213562.Subproblem 1
p + 0.3333333334 = 1.414213562 Simplifying p + 0.3333333334 = 1.414213562 Reorder the terms: 0.3333333334 + p = 1.414213562 Solving 0.3333333334 + p = 1.414213562 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + p = 1.414213562 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + p = 1.414213562 + -0.3333333334 p = 1.414213562 + -0.3333333334 Combine like terms: 1.414213562 + -0.3333333334 = 1.0808802286 p = 1.0808802286 Simplifying p = 1.0808802286Subproblem 2
p + 0.3333333334 = -1.414213562 Simplifying p + 0.3333333334 = -1.414213562 Reorder the terms: 0.3333333334 + p = -1.414213562 Solving 0.3333333334 + p = -1.414213562 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + p = -1.414213562 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + p = -1.414213562 + -0.3333333334 p = -1.414213562 + -0.3333333334 Combine like terms: -1.414213562 + -0.3333333334 = -1.7475468954 p = -1.7475468954 Simplifying p = -1.7475468954Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.0808802286, -1.7475468954}
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