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Simplifying p2 + -9p + -100 = 0 Reorder the terms: -100 + -9p + p2 = 0 Solving -100 + -9p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -9p + 100 + p2 = 0 + 100 Reorder the terms: -100 + 100 + -9p + p2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -9p + p2 = 0 + 100 -9p + p2 = 0 + 100 Combine like terms: 0 + 100 = 100 -9p + p2 = 100 The p term is -9p. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9p + 20.25 + p2 = 100 + 20.25 Reorder the terms: 20.25 + -9p + p2 = 100 + 20.25 Combine like terms: 100 + 20.25 = 120.25 20.25 + -9p + p2 = 120.25 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (p + -4.5) equal to 10.9658561 and -10.9658561.Subproblem 1
p + -4.5 = 10.9658561 Simplifying p + -4.5 = 10.9658561 Reorder the terms: -4.5 + p = 10.9658561 Solving -4.5 + p = 10.9658561 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = 10.9658561 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 10.9658561 + 4.5 p = 10.9658561 + 4.5 Combine like terms: 10.9658561 + 4.5 = 15.4658561 p = 15.4658561 Simplifying p = 15.4658561Subproblem 2
p + -4.5 = -10.9658561 Simplifying p + -4.5 = -10.9658561 Reorder the terms: -4.5 + p = -10.9658561 Solving -4.5 + p = -10.9658561 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = -10.9658561 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -10.9658561 + 4.5 p = -10.9658561 + 4.5 Combine like terms: -10.9658561 + 4.5 = -6.4658561 p = -6.4658561 Simplifying p = -6.4658561Solution
The solution to the problem is based on the solutions from the subproblems. p = {15.4658561, -6.4658561}
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