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Simplifying -3p2 + -60p = -123 Reorder the terms: -60p + -3p2 = -123 Solving -60p + -3p2 = -123 Solving for variable 'p'. Reorder the terms: 123 + -60p + -3p2 = -123 + 123 Combine like terms: -123 + 123 = 0 123 + -60p + -3p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(41 + -20p + -1p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(41 + -20p + -1p2)' equal to zero and attempt to solve: Simplifying 41 + -20p + -1p2 = 0 Solving 41 + -20p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -41 + 20p + p2 = 0 Move the constant term to the right: Add '41' to each side of the equation. -41 + 20p + 41 + p2 = 0 + 41 Reorder the terms: -41 + 41 + 20p + p2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 20p + p2 = 0 + 41 20p + p2 = 0 + 41 Combine like terms: 0 + 41 = 41 20p + p2 = 41 The p term is 20p. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20p + 100 + p2 = 41 + 100 Reorder the terms: 100 + 20p + p2 = 41 + 100 Combine like terms: 41 + 100 = 141 100 + 20p + p2 = 141 Factor a perfect square on the left side: (p + 10)(p + 10) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (p + 10) equal to 11.874342087 and -11.874342087.Subproblem 1
p + 10 = 11.874342087 Simplifying p + 10 = 11.874342087 Reorder the terms: 10 + p = 11.874342087 Solving 10 + p = 11.874342087 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + p = 11.874342087 + -10 Combine like terms: 10 + -10 = 0 0 + p = 11.874342087 + -10 p = 11.874342087 + -10 Combine like terms: 11.874342087 + -10 = 1.874342087 p = 1.874342087 Simplifying p = 1.874342087Subproblem 2
p + 10 = -11.874342087 Simplifying p + 10 = -11.874342087 Reorder the terms: 10 + p = -11.874342087 Solving 10 + p = -11.874342087 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + p = -11.874342087 + -10 Combine like terms: 10 + -10 = 0 0 + p = -11.874342087 + -10 p = -11.874342087 + -10 Combine like terms: -11.874342087 + -10 = -21.874342087 p = -21.874342087 Simplifying p = -21.874342087Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.874342087, -21.874342087}Solution
p = {1.874342087, -21.874342087}
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