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Simplifying -12p2 + 150p = 468.75 Reorder the terms: 150p + -12p2 = 468.75 Solving 150p + -12p2 = 468.75 Solving for variable 'p'. Reorder the terms: -468.75 + 150p + -12p2 = 468.75 + -468.75 Combine like terms: 468.75 + -468.75 = 0.00 -468.75 + 150p + -12p2 = 0.00 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 39.0625 + -12.5p + p2 = 0.00 Move the constant term to the right: Add '-39.0625' to each side of the equation. 39.0625 + -12.5p + -39.0625 + p2 = 0.00 + -39.0625 Reorder the terms: 39.0625 + -39.0625 + -12.5p + p2 = 0.00 + -39.0625 Combine like terms: 39.0625 + -39.0625 = 0.0000 0.0000 + -12.5p + p2 = 0.00 + -39.0625 -12.5p + p2 = 0.00 + -39.0625 Combine like terms: 0.00 + -39.0625 = -39.0625 -12.5p + p2 = -39.0625 The p term is -12.5p. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5p + 39.0625 + p2 = -39.0625 + 39.0625 Reorder the terms: 39.0625 + -12.5p + p2 = -39.0625 + 39.0625 Combine like terms: -39.0625 + 39.0625 = 0.0000 39.0625 + -12.5p + p2 = 0.0000 Factor a perfect square on the left side: (p + -6.25)(p + -6.25) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (p + -6.25) equal to 0.0000 and 0.0000.Subproblem 1
p + -6.25 = 0.0000 Simplifying p + -6.25 = 0.0000 Reorder the terms: -6.25 + p = 0.0000 Solving -6.25 + p = 0.0000 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + p = 0.0000 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + p = 0.0000 + 6.25 p = 0.0000 + 6.25 Combine like terms: 0.0000 + 6.25 = 6.25 p = 6.25 Simplifying p = 6.25Subproblem 2
p + -6.25 = 0.0000 Simplifying p + -6.25 = 0.0000 Reorder the terms: -6.25 + p = 0.0000 Solving -6.25 + p = 0.0000 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + p = 0.0000 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + p = 0.0000 + 6.25 p = 0.0000 + 6.25 Combine like terms: 0.0000 + 6.25 = 6.25 p = 6.25 Simplifying p = 6.25Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.25, 6.25}
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