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Simplifying -2p2 + -5p + 1 = 7p2 + p Reorder the terms: 1 + -5p + -2p2 = 7p2 + p Reorder the terms: 1 + -5p + -2p2 = p + 7p2 Solving 1 + -5p + -2p2 = p + 7p2 Solving for variable 'p'. Reorder the terms: 1 + -5p + -1p + -2p2 + -7p2 = p + 7p2 + -1p + -7p2 Combine like terms: -5p + -1p = -6p 1 + -6p + -2p2 + -7p2 = p + 7p2 + -1p + -7p2 Combine like terms: -2p2 + -7p2 = -9p2 1 + -6p + -9p2 = p + 7p2 + -1p + -7p2 Reorder the terms: 1 + -6p + -9p2 = p + -1p + 7p2 + -7p2 Combine like terms: p + -1p = 0 1 + -6p + -9p2 = 0 + 7p2 + -7p2 1 + -6p + -9p2 = 7p2 + -7p2 Combine like terms: 7p2 + -7p2 = 0 1 + -6p + -9p2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.1111111111 + 0.6666666667p + p2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.6666666667p + 0.1111111111 + p2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 0.6666666667p + p2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 0.6666666667p + p2 = 0 + 0.1111111111 0.6666666667p + p2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 0.6666666667p + p2 = 0.1111111111 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 = 0.1111111111 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667p + p2 = 0.1111111111 + 0.1111111112 Combine like terms: 0.1111111111 + 0.1111111112 = 0.2222222223 0.1111111112 + 0.6666666667p + p2 = 0.2222222223 Factor a perfect square on the left side: (p + 0.3333333334)(p + 0.3333333334) = 0.2222222223 Calculate the square root of the right side: 0.471404521 Break this problem into two subproblems by setting (p + 0.3333333334) equal to 0.471404521 and -0.471404521.Subproblem 1
p + 0.3333333334 = 0.471404521 Simplifying p + 0.3333333334 = 0.471404521 Reorder the terms: 0.3333333334 + p = 0.471404521 Solving 0.3333333334 + p = 0.471404521 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 = 0.471404521 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + p = 0.471404521 + -0.3333333334 p = 0.471404521 + -0.3333333334 Combine like terms: 0.471404521 + -0.3333333334 = 0.1380711876 p = 0.1380711876 Simplifying p = 0.1380711876Subproblem 2
p + 0.3333333334 = -0.471404521 Simplifying p + 0.3333333334 = -0.471404521 Reorder the terms: 0.3333333334 + p = -0.471404521 Solving 0.3333333334 + p = -0.471404521 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 = -0.471404521 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + p = -0.471404521 + -0.3333333334 p = -0.471404521 + -0.3333333334 Combine like terms: -0.471404521 + -0.3333333334 = -0.8047378544 p = -0.8047378544 Simplifying p = -0.8047378544Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.1380711876, -0.8047378544}
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