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Simplifying 120 = p2 + 22p Reorder the terms: 120 = 22p + p2 Solving 120 = 22p + p2 Solving for variable 'p'. Reorder the terms: 120 + -22p + -1p2 = 22p + -22p + p2 + -1p2 Combine like terms: 22p + -22p = 0 120 + -22p + -1p2 = 0 + p2 + -1p2 120 + -22p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 120 + -22p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -120 + 22p + p2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 22p + 120 + p2 = 0 + 120 Reorder the terms: -120 + 120 + 22p + p2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 22p + p2 = 0 + 120 22p + p2 = 0 + 120 Combine like terms: 0 + 120 = 120 22p + p2 = 120 The p term is 22p. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22p + 121 + p2 = 120 + 121 Reorder the terms: 121 + 22p + p2 = 120 + 121 Combine like terms: 120 + 121 = 241 121 + 22p + p2 = 241 Factor a perfect square on the left side: (p + 11)(p + 11) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (p + 11) equal to 15.524174696 and -15.524174696.Subproblem 1
p + 11 = 15.524174696 Simplifying p + 11 = 15.524174696 Reorder the terms: 11 + p = 15.524174696 Solving 11 + p = 15.524174696 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + p = 15.524174696 + -11 Combine like terms: 11 + -11 = 0 0 + p = 15.524174696 + -11 p = 15.524174696 + -11 Combine like terms: 15.524174696 + -11 = 4.524174696 p = 4.524174696 Simplifying p = 4.524174696Subproblem 2
p + 11 = -15.524174696 Simplifying p + 11 = -15.524174696 Reorder the terms: 11 + p = -15.524174696 Solving 11 + p = -15.524174696 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + p = -15.524174696 + -11 Combine like terms: 11 + -11 = 0 0 + p = -15.524174696 + -11 p = -15.524174696 + -11 Combine like terms: -15.524174696 + -11 = -26.524174696 p = -26.524174696 Simplifying p = -26.524174696Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.524174696, -26.524174696}
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