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Simplifying -6p2 + 120000p = 1500000 Reorder the terms: 120000p + -6p2 = 1500000 Solving 120000p + -6p2 = 1500000 Solving for variable 'p'. Reorder the terms: -1500000 + 120000p + -6p2 = 1500000 + -1500000 Combine like terms: 1500000 + -1500000 = 0 -1500000 + 120000p + -6p2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-250000 + 20000p + -1p2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-250000 + 20000p + -1p2)' equal to zero and attempt to solve: Simplifying -250000 + 20000p + -1p2 = 0 Solving -250000 + 20000p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 250000 + -20000p + p2 = 0 Move the constant term to the right: Add '-250000' to each side of the equation. 250000 + -20000p + -250000 + p2 = 0 + -250000 Reorder the terms: 250000 + -250000 + -20000p + p2 = 0 + -250000 Combine like terms: 250000 + -250000 = 0 0 + -20000p + p2 = 0 + -250000 -20000p + p2 = 0 + -250000 Combine like terms: 0 + -250000 = -250000 -20000p + p2 = -250000 The p term is -20000p. Take half its coefficient (-10000). Square it (100000000) and add it to both sides. Add '100000000' to each side of the equation. -20000p + 100000000 + p2 = -250000 + 100000000 Reorder the terms: 100000000 + -20000p + p2 = -250000 + 100000000 Combine like terms: -250000 + 100000000 = 99750000 100000000 + -20000p + p2 = 99750000 Factor a perfect square on the left side: (p + -10000)(p + -10000) = 99750000 Calculate the square root of the right side: 9987.492177719 Break this problem into two subproblems by setting (p + -10000) equal to 9987.492177719 and -9987.492177719.Subproblem 1
p + -10000 = 9987.492177719 Simplifying p + -10000 = 9987.492177719 Reorder the terms: -10000 + p = 9987.492177719 Solving -10000 + p = 9987.492177719 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10000' to each side of the equation. -10000 + 10000 + p = 9987.492177719 + 10000 Combine like terms: -10000 + 10000 = 0 0 + p = 9987.492177719 + 10000 p = 9987.492177719 + 10000 Combine like terms: 9987.492177719 + 10000 = 19987.492177719 p = 19987.492177719 Simplifying p = 19987.492177719Subproblem 2
p + -10000 = -9987.492177719 Simplifying p + -10000 = -9987.492177719 Reorder the terms: -10000 + p = -9987.492177719 Solving -10000 + p = -9987.492177719 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10000' to each side of the equation. -10000 + 10000 + p = -9987.492177719 + 10000 Combine like terms: -10000 + 10000 = 0 0 + p = -9987.492177719 + 10000 p = -9987.492177719 + 10000 Combine like terms: -9987.492177719 + 10000 = 12.507822281 p = 12.507822281 Simplifying p = 12.507822281Solution
The solution to the problem is based on the solutions from the subproblems. p = {19987.492177719, 12.507822281}Solution
p = {19987.492177719, 12.507822281}
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