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Simplifying 24p2 + -28p + -8 = 0 Reorder the terms: -8 + -28p + 24p2 = 0 Solving -8 + -28p + 24p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + -7p + 6p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -7p + 6p2)' equal to zero and attempt to solve: Simplifying -2 + -7p + 6p2 = 0 Solving -2 + -7p + 6p2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.3333333333 + -1.166666667p + p2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -1.166666667p + 0.3333333333 + p2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -1.166666667p + p2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -1.166666667p + p2 = 0 + 0.3333333333 -1.166666667p + p2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -1.166666667p + p2 = 0.3333333333 The p term is -1.166666667p. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667p + 0.3402777780 + p2 = 0.3333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667p + p2 = 0.3333333333 + 0.3402777780 Combine like terms: 0.3333333333 + 0.3402777780 = 0.6736111113 0.3402777780 + -1.166666667p + p2 = 0.6736111113 Factor a perfect square on the left side: (p + -0.5833333335)(p + -0.5833333335) = 0.6736111113 Calculate the square root of the right side: 0.82073815 Break this problem into two subproblems by setting (p + -0.5833333335) equal to 0.82073815 and -0.82073815.Subproblem 1
p + -0.5833333335 = 0.82073815 Simplifying p + -0.5833333335 = 0.82073815 Reorder the terms: -0.5833333335 + p = 0.82073815 Solving -0.5833333335 + p = 0.82073815 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + p = 0.82073815 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + p = 0.82073815 + 0.5833333335 p = 0.82073815 + 0.5833333335 Combine like terms: 0.82073815 + 0.5833333335 = 1.4040714835 p = 1.4040714835 Simplifying p = 1.4040714835Subproblem 2
p + -0.5833333335 = -0.82073815 Simplifying p + -0.5833333335 = -0.82073815 Reorder the terms: -0.5833333335 + p = -0.82073815 Solving -0.5833333335 + p = -0.82073815 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + p = -0.82073815 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + p = -0.82073815 + 0.5833333335 p = -0.82073815 + 0.5833333335 Combine like terms: -0.82073815 + 0.5833333335 = -0.2374048165 p = -0.2374048165 Simplifying p = -0.2374048165Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.4040714835, -0.2374048165}Solution
p = {1.4040714835, -0.2374048165}
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