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Simplifying 22p2 + 34p + -36 = 0 Reorder the terms: -36 + 34p + 22p2 = 0 Solving -36 + 34p + 22p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 17p + 11p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 17p + 11p2)' equal to zero and attempt to solve: Simplifying -18 + 17p + 11p2 = 0 Solving -18 + 17p + 11p2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.636363636 + 1.545454545p + p2 = 0 Move the constant term to the right: Add '1.636363636' to each side of the equation. -1.636363636 + 1.545454545p + 1.636363636 + p2 = 0 + 1.636363636 Reorder the terms: -1.636363636 + 1.636363636 + 1.545454545p + p2 = 0 + 1.636363636 Combine like terms: -1.636363636 + 1.636363636 = 0.000000000 0.000000000 + 1.545454545p + p2 = 0 + 1.636363636 1.545454545p + p2 = 0 + 1.636363636 Combine like terms: 0 + 1.636363636 = 1.636363636 1.545454545p + p2 = 1.636363636 The p term is 1.545454545p. Take half its coefficient (0.7727272725). Square it (0.5971074377) and add it to both sides. Add '0.5971074377' to each side of the equation. 1.545454545p + 0.5971074377 + p2 = 1.636363636 + 0.5971074377 Reorder the terms: 0.5971074377 + 1.545454545p + p2 = 1.636363636 + 0.5971074377 Combine like terms: 1.636363636 + 0.5971074377 = 2.2334710737 0.5971074377 + 1.545454545p + p2 = 2.2334710737 Factor a perfect square on the left side: (p + 0.7727272725)(p + 0.7727272725) = 2.2334710737 Calculate the square root of the right side: 1.494480202 Break this problem into two subproblems by setting (p + 0.7727272725) equal to 1.494480202 and -1.494480202.Subproblem 1
p + 0.7727272725 = 1.494480202 Simplifying p + 0.7727272725 = 1.494480202 Reorder the terms: 0.7727272725 + p = 1.494480202 Solving 0.7727272725 + p = 1.494480202 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.7727272725' to each side of the equation. 0.7727272725 + -0.7727272725 + p = 1.494480202 + -0.7727272725 Combine like terms: 0.7727272725 + -0.7727272725 = 0.0000000000 0.0000000000 + p = 1.494480202 + -0.7727272725 p = 1.494480202 + -0.7727272725 Combine like terms: 1.494480202 + -0.7727272725 = 0.7217529295 p = 0.7217529295 Simplifying p = 0.7217529295Subproblem 2
p + 0.7727272725 = -1.494480202 Simplifying p + 0.7727272725 = -1.494480202 Reorder the terms: 0.7727272725 + p = -1.494480202 Solving 0.7727272725 + p = -1.494480202 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.7727272725' to each side of the equation. 0.7727272725 + -0.7727272725 + p = -1.494480202 + -0.7727272725 Combine like terms: 0.7727272725 + -0.7727272725 = 0.0000000000 0.0000000000 + p = -1.494480202 + -0.7727272725 p = -1.494480202 + -0.7727272725 Combine like terms: -1.494480202 + -0.7727272725 = -2.2672074745 p = -2.2672074745 Simplifying p = -2.2672074745Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.7217529295, -2.2672074745}Solution
p = {0.7217529295, -2.2672074745}
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