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Simplifying 9p2 + -42p + -20 = -29 Reorder the terms: -20 + -42p + 9p2 = -29 Solving -20 + -42p + 9p2 = -29 Solving for variable 'p'. Reorder the terms: -20 + 29 + -42p + 9p2 = -29 + 29 Combine like terms: -20 + 29 = 9 9 + -42p + 9p2 = -29 + 29 Combine like terms: -29 + 29 = 0 9 + -42p + 9p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -14p + 3p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -14p + 3p2)' equal to zero and attempt to solve: Simplifying 3 + -14p + 3p2 = 0 Solving 3 + -14p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -4.666666667p + p2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.666666667p + -1 + p2 = 0 + -1 Reorder the terms: 1 + -1 + -4.666666667p + p2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.666666667p + p2 = 0 + -1 -4.666666667p + p2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.666666667p + p2 = -1 The p term is -4.666666667p. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667p + 5.444444448 + p2 = -1 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667p + p2 = -1 + 5.444444448 Combine like terms: -1 + 5.444444448 = 4.444444448 5.444444448 + -4.666666667p + p2 = 4.444444448 Factor a perfect square on the left side: (p + -2.333333334)(p + -2.333333334) = 4.444444448 Calculate the square root of the right side: 2.108185108 Break this problem into two subproblems by setting (p + -2.333333334) equal to 2.108185108 and -2.108185108.Subproblem 1
p + -2.333333334 = 2.108185108 Simplifying p + -2.333333334 = 2.108185108 Reorder the terms: -2.333333334 + p = 2.108185108 Solving -2.333333334 + p = 2.108185108 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + p = 2.108185108 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + p = 2.108185108 + 2.333333334 p = 2.108185108 + 2.333333334 Combine like terms: 2.108185108 + 2.333333334 = 4.441518442 p = 4.441518442 Simplifying p = 4.441518442Subproblem 2
p + -2.333333334 = -2.108185108 Simplifying p + -2.333333334 = -2.108185108 Reorder the terms: -2.333333334 + p = -2.108185108 Solving -2.333333334 + p = -2.108185108 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + p = -2.108185108 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + p = -2.108185108 + 2.333333334 p = -2.108185108 + 2.333333334 Combine like terms: -2.108185108 + 2.333333334 = 0.225148226 p = 0.225148226 Simplifying p = 0.225148226Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.441518442, 0.225148226}Solution
p = {4.441518442, 0.225148226}
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