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Simplifying (44p + -3p)(p + -3) = 3 Combine like terms: 44p + -3p = 41p (41p)(p + -3) = 3 Remove parenthesis around (41p) 41p(p + -3) = 3 Reorder the terms: 41p(-3 + p) = 3 (-3 * 41p + p * 41p) = 3 (-123p + 41p2) = 3 Solving -123p + 41p2 = 3 Solving for variable 'p'. Reorder the terms: -3 + -123p + 41p2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -123p + 41p2 = 0 Begin completing the square. Divide all terms by 41 the coefficient of the squared term: Divide each side by '41'. -0.07317073171 + -3p + p2 = 0 Move the constant term to the right: Add '0.07317073171' to each side of the equation. -0.07317073171 + -3p + 0.07317073171 + p2 = 0 + 0.07317073171 Reorder the terms: -0.07317073171 + 0.07317073171 + -3p + p2 = 0 + 0.07317073171 Combine like terms: -0.07317073171 + 0.07317073171 = 0.00000000000 0.00000000000 + -3p + p2 = 0 + 0.07317073171 -3p + p2 = 0 + 0.07317073171 Combine like terms: 0 + 0.07317073171 = 0.07317073171 -3p + p2 = 0.07317073171 The p term is -3p. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3p + 2.25 + p2 = 0.07317073171 + 2.25 Reorder the terms: 2.25 + -3p + p2 = 0.07317073171 + 2.25 Combine like terms: 0.07317073171 + 2.25 = 2.32317073171 2.25 + -3p + p2 = 2.32317073171 Factor a perfect square on the left side: (p + -1.5)(p + -1.5) = 2.32317073171 Calculate the square root of the right side: 1.524195109 Break this problem into two subproblems by setting (p + -1.5) equal to 1.524195109 and -1.524195109.Subproblem 1
p + -1.5 = 1.524195109 Simplifying p + -1.5 = 1.524195109 Reorder the terms: -1.5 + p = 1.524195109 Solving -1.5 + p = 1.524195109 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = 1.524195109 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = 1.524195109 + 1.5 p = 1.524195109 + 1.5 Combine like terms: 1.524195109 + 1.5 = 3.024195109 p = 3.024195109 Simplifying p = 3.024195109Subproblem 2
p + -1.5 = -1.524195109 Simplifying p + -1.5 = -1.524195109 Reorder the terms: -1.5 + p = -1.524195109 Solving -1.5 + p = -1.524195109 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = -1.524195109 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = -1.524195109 + 1.5 p = -1.524195109 + 1.5 Combine like terms: -1.524195109 + 1.5 = -0.024195109 p = -0.024195109 Simplifying p = -0.024195109Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.024195109, -0.024195109}
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