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Simplifying 4p2 + -68p = -200 Reorder the terms: -68p + 4p2 = -200 Solving -68p + 4p2 = -200 Solving for variable 'p'. Reorder the terms: 200 + -68p + 4p2 = -200 + 200 Combine like terms: -200 + 200 = 0 200 + -68p + 4p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(50 + -17p + p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(50 + -17p + p2)' equal to zero and attempt to solve: Simplifying 50 + -17p + p2 = 0 Solving 50 + -17p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -17p + -50 + p2 = 0 + -50 Reorder the terms: 50 + -50 + -17p + p2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -17p + p2 = 0 + -50 -17p + p2 = 0 + -50 Combine like terms: 0 + -50 = -50 -17p + p2 = -50 The p term is -17p. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17p + 72.25 + p2 = -50 + 72.25 Reorder the terms: 72.25 + -17p + p2 = -50 + 72.25 Combine like terms: -50 + 72.25 = 22.25 72.25 + -17p + p2 = 22.25 Factor a perfect square on the left side: (p + -8.5)(p + -8.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (p + -8.5) equal to 4.716990566 and -4.716990566.Subproblem 1
p + -8.5 = 4.716990566 Simplifying p + -8.5 = 4.716990566 Reorder the terms: -8.5 + p = 4.716990566 Solving -8.5 + p = 4.716990566 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + p = 4.716990566 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + p = 4.716990566 + 8.5 p = 4.716990566 + 8.5 Combine like terms: 4.716990566 + 8.5 = 13.216990566 p = 13.216990566 Simplifying p = 13.216990566Subproblem 2
p + -8.5 = -4.716990566 Simplifying p + -8.5 = -4.716990566 Reorder the terms: -8.5 + p = -4.716990566 Solving -8.5 + p = -4.716990566 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + p = -4.716990566 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + p = -4.716990566 + 8.5 p = -4.716990566 + 8.5 Combine like terms: -4.716990566 + 8.5 = 3.783009434 p = 3.783009434 Simplifying p = 3.783009434Solution
The solution to the problem is based on the solutions from the subproblems. p = {13.216990566, 3.783009434}Solution
p = {13.216990566, 3.783009434}
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