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Simplifying (132 + -3p)(p + -6) = 6 Reorder the terms: (132 + -3p)(-6 + p) = 6 Multiply (132 + -3p) * (-6 + p) (132(-6 + p) + -3p * (-6 + p)) = 6 ((-6 * 132 + p * 132) + -3p * (-6 + p)) = 6 ((-792 + 132p) + -3p * (-6 + p)) = 6 (-792 + 132p + (-6 * -3p + p * -3p)) = 6 (-792 + 132p + (18p + -3p2)) = 6 Combine like terms: 132p + 18p = 150p (-792 + 150p + -3p2) = 6 Solving -792 + 150p + -3p2 = 6 Solving for variable 'p'. Reorder the terms: -792 + -6 + 150p + -3p2 = 6 + -6 Combine like terms: -792 + -6 = -798 -798 + 150p + -3p2 = 6 + -6 Combine like terms: 6 + -6 = 0 -798 + 150p + -3p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-266 + 50p + -1p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-266 + 50p + -1p2)' equal to zero and attempt to solve: Simplifying -266 + 50p + -1p2 = 0 Solving -266 + 50p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 266 + -50p + p2 = 0 Move the constant term to the right: Add '-266' to each side of the equation. 266 + -50p + -266 + p2 = 0 + -266 Reorder the terms: 266 + -266 + -50p + p2 = 0 + -266 Combine like terms: 266 + -266 = 0 0 + -50p + p2 = 0 + -266 -50p + p2 = 0 + -266 Combine like terms: 0 + -266 = -266 -50p + p2 = -266 The p term is -50p. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50p + 625 + p2 = -266 + 625 Reorder the terms: 625 + -50p + p2 = -266 + 625 Combine like terms: -266 + 625 = 359 625 + -50p + p2 = 359 Factor a perfect square on the left side: (p + -25)(p + -25) = 359 Calculate the square root of the right side: 18.947295321 Break this problem into two subproblems by setting (p + -25) equal to 18.947295321 and -18.947295321.Subproblem 1
p + -25 = 18.947295321 Simplifying p + -25 = 18.947295321 Reorder the terms: -25 + p = 18.947295321 Solving -25 + p = 18.947295321 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + p = 18.947295321 + 25 Combine like terms: -25 + 25 = 0 0 + p = 18.947295321 + 25 p = 18.947295321 + 25 Combine like terms: 18.947295321 + 25 = 43.947295321 p = 43.947295321 Simplifying p = 43.947295321Subproblem 2
p + -25 = -18.947295321 Simplifying p + -25 = -18.947295321 Reorder the terms: -25 + p = -18.947295321 Solving -25 + p = -18.947295321 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + p = -18.947295321 + 25 Combine like terms: -25 + 25 = 0 0 + p = -18.947295321 + 25 p = -18.947295321 + 25 Combine like terms: -18.947295321 + 25 = 6.052704679 p = 6.052704679 Simplifying p = 6.052704679Solution
The solution to the problem is based on the solutions from the subproblems. p = {43.947295321, 6.052704679}Solution
p = {43.947295321, 6.052704679}
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