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Simplifying 42p2 + -6p + -45 = 0 Reorder the terms: -45 + -6p + 42p2 = 0 Solving -45 + -6p + 42p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + -2p + 14p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-15 + -2p + 14p2)' equal to zero and attempt to solve: Simplifying -15 + -2p + 14p2 = 0 Solving -15 + -2p + 14p2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.071428571 + -0.1428571429p + p2 = 0 Move the constant term to the right: Add '1.071428571' to each side of the equation. -1.071428571 + -0.1428571429p + 1.071428571 + p2 = 0 + 1.071428571 Reorder the terms: -1.071428571 + 1.071428571 + -0.1428571429p + p2 = 0 + 1.071428571 Combine like terms: -1.071428571 + 1.071428571 = 0.000000000 0.000000000 + -0.1428571429p + p2 = 0 + 1.071428571 -0.1428571429p + p2 = 0 + 1.071428571 Combine like terms: 0 + 1.071428571 = 1.071428571 -0.1428571429p + p2 = 1.071428571 The p term is -0.1428571429p. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429p + 0.005102040819 + p2 = 1.071428571 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429p + p2 = 1.071428571 + 0.005102040819 Combine like terms: 1.071428571 + 0.005102040819 = 1.076530611819 0.005102040819 + -0.1428571429p + p2 = 1.076530611819 Factor a perfect square on the left side: (p + -0.07142857145)(p + -0.07142857145) = 1.076530611819 Calculate the square root of the right side: 1.037559932 Break this problem into two subproblems by setting (p + -0.07142857145) equal to 1.037559932 and -1.037559932.Subproblem 1
p + -0.07142857145 = 1.037559932 Simplifying p + -0.07142857145 = 1.037559932 Reorder the terms: -0.07142857145 + p = 1.037559932 Solving -0.07142857145 + p = 1.037559932 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + p = 1.037559932 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + p = 1.037559932 + 0.07142857145 p = 1.037559932 + 0.07142857145 Combine like terms: 1.037559932 + 0.07142857145 = 1.10898850345 p = 1.10898850345 Simplifying p = 1.10898850345Subproblem 2
p + -0.07142857145 = -1.037559932 Simplifying p + -0.07142857145 = -1.037559932 Reorder the terms: -0.07142857145 + p = -1.037559932 Solving -0.07142857145 + p = -1.037559932 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + p = -1.037559932 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + p = -1.037559932 + 0.07142857145 p = -1.037559932 + 0.07142857145 Combine like terms: -1.037559932 + 0.07142857145 = -0.96613136055 p = -0.96613136055 Simplifying p = -0.96613136055Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.10898850345, -0.96613136055}Solution
p = {1.10898850345, -0.96613136055}
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