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Simplifying 7p(p + -9) = 7p + -1(p + -9) + p Reorder the terms: 7p(-9 + p) = 7p + -1(p + -9) + p (-9 * 7p + p * 7p) = 7p + -1(p + -9) + p (-63p + 7p2) = 7p + -1(p + -9) + p Reorder the terms: -63p + 7p2 = 7p + -1(-9 + p) + p -63p + 7p2 = 7p + (-9 * -1 + p * -1) + p -63p + 7p2 = 7p + (9 + -1p) + p Reorder the terms: -63p + 7p2 = 9 + 7p + -1p + p Combine like terms: 7p + -1p = 6p -63p + 7p2 = 9 + 6p + p Combine like terms: 6p + p = 7p -63p + 7p2 = 9 + 7p Solving -63p + 7p2 = 9 + 7p Solving for variable 'p'. Reorder the terms: -9 + -63p + -7p + 7p2 = 9 + 7p + -9 + -7p Combine like terms: -63p + -7p = -70p -9 + -70p + 7p2 = 9 + 7p + -9 + -7p Reorder the terms: -9 + -70p + 7p2 = 9 + -9 + 7p + -7p Combine like terms: 9 + -9 = 0 -9 + -70p + 7p2 = 0 + 7p + -7p -9 + -70p + 7p2 = 7p + -7p Combine like terms: 7p + -7p = 0 -9 + -70p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + -10p + p2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -10p + 1.285714286 + p2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -10p + p2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -10p + p2 = 0 + 1.285714286 -10p + p2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -10p + p2 = 1.285714286 The p term is -10p. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10p + 25 + p2 = 1.285714286 + 25 Reorder the terms: 25 + -10p + p2 = 1.285714286 + 25 Combine like terms: 1.285714286 + 25 = 26.285714286 25 + -10p + p2 = 26.285714286 Factor a perfect square on the left side: (p + -5)(p + -5) = 26.285714286 Calculate the square root of the right side: 5.126959556 Break this problem into two subproblems by setting (p + -5) equal to 5.126959556 and -5.126959556.Subproblem 1
p + -5 = 5.126959556 Simplifying p + -5 = 5.126959556 Reorder the terms: -5 + p = 5.126959556 Solving -5 + p = 5.126959556 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = 5.126959556 + 5 Combine like terms: -5 + 5 = 0 0 + p = 5.126959556 + 5 p = 5.126959556 + 5 Combine like terms: 5.126959556 + 5 = 10.126959556 p = 10.126959556 Simplifying p = 10.126959556Subproblem 2
p + -5 = -5.126959556 Simplifying p + -5 = -5.126959556 Reorder the terms: -5 + p = -5.126959556 Solving -5 + p = -5.126959556 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = -5.126959556 + 5 Combine like terms: -5 + 5 = 0 0 + p = -5.126959556 + 5 p = -5.126959556 + 5 Combine like terms: -5.126959556 + 5 = -0.126959556 p = -0.126959556 Simplifying p = -0.126959556Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.126959556, -0.126959556}
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