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Simplifying (44 + -3p)(p + -3) = 3 Reorder the terms: (44 + -3p)(-3 + p) = 3 Multiply (44 + -3p) * (-3 + p) (44(-3 + p) + -3p * (-3 + p)) = 3 ((-3 * 44 + p * 44) + -3p * (-3 + p)) = 3 ((-132 + 44p) + -3p * (-3 + p)) = 3 (-132 + 44p + (-3 * -3p + p * -3p)) = 3 (-132 + 44p + (9p + -3p2)) = 3 Combine like terms: 44p + 9p = 53p (-132 + 53p + -3p2) = 3 Solving -132 + 53p + -3p2 = 3 Solving for variable 'p'. Reorder the terms: -132 + -3 + 53p + -3p2 = 3 + -3 Combine like terms: -132 + -3 = -135 -135 + 53p + -3p2 = 3 + -3 Combine like terms: 3 + -3 = 0 -135 + 53p + -3p2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 45 + -17.66666667p + p2 = 0 Move the constant term to the right: Add '-45' to each side of the equation. 45 + -17.66666667p + -45 + p2 = 0 + -45 Reorder the terms: 45 + -45 + -17.66666667p + p2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -17.66666667p + p2 = 0 + -45 -17.66666667p + p2 = 0 + -45 Combine like terms: 0 + -45 = -45 -17.66666667p + p2 = -45 The p term is -17.66666667p. Take half its coefficient (-8.833333335). Square it (78.02777781) and add it to both sides. Add '78.02777781' to each side of the equation. -17.66666667p + 78.02777781 + p2 = -45 + 78.02777781 Reorder the terms: 78.02777781 + -17.66666667p + p2 = -45 + 78.02777781 Combine like terms: -45 + 78.02777781 = 33.02777781 78.02777781 + -17.66666667p + p2 = 33.02777781 Factor a perfect square on the left side: (p + -8.833333335)(p + -8.833333335) = 33.02777781 Calculate the square root of the right side: 5.746979886 Break this problem into two subproblems by setting (p + -8.833333335) equal to 5.746979886 and -5.746979886.Subproblem 1
p + -8.833333335 = 5.746979886 Simplifying p + -8.833333335 = 5.746979886 Reorder the terms: -8.833333335 + p = 5.746979886 Solving -8.833333335 + p = 5.746979886 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8.833333335' to each side of the equation. -8.833333335 + 8.833333335 + p = 5.746979886 + 8.833333335 Combine like terms: -8.833333335 + 8.833333335 = 0.000000000 0.000000000 + p = 5.746979886 + 8.833333335 p = 5.746979886 + 8.833333335 Combine like terms: 5.746979886 + 8.833333335 = 14.580313221 p = 14.580313221 Simplifying p = 14.580313221Subproblem 2
p + -8.833333335 = -5.746979886 Simplifying p + -8.833333335 = -5.746979886 Reorder the terms: -8.833333335 + p = -5.746979886 Solving -8.833333335 + p = -5.746979886 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8.833333335' to each side of the equation. -8.833333335 + 8.833333335 + p = -5.746979886 + 8.833333335 Combine like terms: -8.833333335 + 8.833333335 = 0.000000000 0.000000000 + p = -5.746979886 + 8.833333335 p = -5.746979886 + 8.833333335 Combine like terms: -5.746979886 + 8.833333335 = 3.086353449 p = 3.086353449 Simplifying p = 3.086353449Solution
The solution to the problem is based on the solutions from the subproblems. p = {14.580313221, 3.086353449}
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