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Simplifying 18p2 + -22p + -21 = 0 Reorder the terms: -21 + -22p + 18p2 = 0 Solving -21 + -22p + 18p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -1.166666667 + -1.222222222p + p2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -1.222222222p + 1.166666667 + p2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -1.222222222p + p2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -1.222222222p + p2 = 0 + 1.166666667 -1.222222222p + p2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -1.222222222p + p2 = 1.166666667 The p term is -1.222222222p. Take half its coefficient (-0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. -1.222222222p + 0.3734567900 + p2 = 1.166666667 + 0.3734567900 Reorder the terms: 0.3734567900 + -1.222222222p + p2 = 1.166666667 + 0.3734567900 Combine like terms: 1.166666667 + 0.3734567900 = 1.540123457 0.3734567900 + -1.222222222p + p2 = 1.540123457 Factor a perfect square on the left side: (p + -0.611111111)(p + -0.611111111) = 1.540123457 Calculate the square root of the right side: 1.241017106 Break this problem into two subproblems by setting (p + -0.611111111) equal to 1.241017106 and -1.241017106.Subproblem 1
p + -0.611111111 = 1.241017106 Simplifying p + -0.611111111 = 1.241017106 Reorder the terms: -0.611111111 + p = 1.241017106 Solving -0.611111111 + p = 1.241017106 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + p = 1.241017106 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + p = 1.241017106 + 0.611111111 p = 1.241017106 + 0.611111111 Combine like terms: 1.241017106 + 0.611111111 = 1.852128217 p = 1.852128217 Simplifying p = 1.852128217Subproblem 2
p + -0.611111111 = -1.241017106 Simplifying p + -0.611111111 = -1.241017106 Reorder the terms: -0.611111111 + p = -1.241017106 Solving -0.611111111 + p = -1.241017106 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + p = -1.241017106 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + p = -1.241017106 + 0.611111111 p = -1.241017106 + 0.611111111 Combine like terms: -1.241017106 + 0.611111111 = -0.629905995 p = -0.629905995 Simplifying p = -0.629905995Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.852128217, -0.629905995}
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