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Simplifying 21p2 + 30p + -40 = 0 Reorder the terms: -40 + 30p + 21p2 = 0 Solving -40 + 30p + 21p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.904761905 + 1.428571429p + p2 = 0 Move the constant term to the right: Add '1.904761905' to each side of the equation. -1.904761905 + 1.428571429p + 1.904761905 + p2 = 0 + 1.904761905 Reorder the terms: -1.904761905 + 1.904761905 + 1.428571429p + p2 = 0 + 1.904761905 Combine like terms: -1.904761905 + 1.904761905 = 0.000000000 0.000000000 + 1.428571429p + p2 = 0 + 1.904761905 1.428571429p + p2 = 0 + 1.904761905 Combine like terms: 0 + 1.904761905 = 1.904761905 1.428571429p + p2 = 1.904761905 The p term is 1.428571429p. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429p + 0.5102040819 + p2 = 1.904761905 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429p + p2 = 1.904761905 + 0.5102040819 Combine like terms: 1.904761905 + 0.5102040819 = 2.4149659869 0.5102040819 + 1.428571429p + p2 = 2.4149659869 Factor a perfect square on the left side: (p + 0.7142857145)(p + 0.7142857145) = 2.4149659869 Calculate the square root of the right side: 1.554016083 Break this problem into two subproblems by setting (p + 0.7142857145) equal to 1.554016083 and -1.554016083.Subproblem 1
p + 0.7142857145 = 1.554016083 Simplifying p + 0.7142857145 = 1.554016083 Reorder the terms: 0.7142857145 + p = 1.554016083 Solving 0.7142857145 + p = 1.554016083 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + p = 1.554016083 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + p = 1.554016083 + -0.7142857145 p = 1.554016083 + -0.7142857145 Combine like terms: 1.554016083 + -0.7142857145 = 0.8397303685 p = 0.8397303685 Simplifying p = 0.8397303685Subproblem 2
p + 0.7142857145 = -1.554016083 Simplifying p + 0.7142857145 = -1.554016083 Reorder the terms: 0.7142857145 + p = -1.554016083 Solving 0.7142857145 + p = -1.554016083 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + p = -1.554016083 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + p = -1.554016083 + -0.7142857145 p = -1.554016083 + -0.7142857145 Combine like terms: -1.554016083 + -0.7142857145 = -2.2683017975 p = -2.2683017975 Simplifying p = -2.2683017975Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.8397303685, -2.2683017975}
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