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Simplifying 0.07p + 0.09p(7000 + -1p) = 530 0.07p + (7000 * 0.09p + -1p * 0.09p) = 530 0.07p + (630p + -0.09p2) = 530 Combine like terms: 0.07p + 630p = 630.07p 630.07p + -0.09p2 = 530 Solving 630.07p + -0.09p2 = 530 Solving for variable 'p'. Reorder the terms: -530 + 630.07p + -0.09p2 = 530 + -530 Combine like terms: 530 + -530 = 0 -530 + 630.07p + -0.09p2 = 0 Begin completing the square. Divide all terms by -0.09 the coefficient of the squared term: Divide each side by '-0.09'. 5888.888889 + -7000.777778p + p2 = 0 Move the constant term to the right: Add '-5888.888889' to each side of the equation. 5888.888889 + -7000.777778p + -5888.888889 + p2 = 0 + -5888.888889 Reorder the terms: 5888.888889 + -5888.888889 + -7000.777778p + p2 = 0 + -5888.888889 Combine like terms: 5888.888889 + -5888.888889 = 0.000000 0.000000 + -7000.777778p + p2 = 0 + -5888.888889 -7000.777778p + p2 = 0 + -5888.888889 Combine like terms: 0 + -5888.888889 = -5888.888889 -7000.777778p + p2 = -5888.888889 The p term is -7000.777778p. Take half its coefficient (-3500.388889). Square it (12252722.37) and add it to both sides. Add '12252722.37' to each side of the equation. -7000.777778p + 12252722.37 + p2 = -5888.888889 + 12252722.37 Reorder the terms: 12252722.37 + -7000.777778p + p2 = -5888.888889 + 12252722.37 Combine like terms: -5888.888889 + 12252722.37 = 12246833.481111 12252722.37 + -7000.777778p + p2 = 12246833.481111 Factor a perfect square on the left side: (p + -3500.388889)(p + -3500.388889) = 12246833.481111 Calculate the square root of the right side: 3499.547610922 Break this problem into two subproblems by setting (p + -3500.388889) equal to 3499.547610922 and -3499.547610922.Subproblem 1
p + -3500.388889 = 3499.547610922 Simplifying p + -3500.388889 = 3499.547610922 Reorder the terms: -3500.388889 + p = 3499.547610922 Solving -3500.388889 + p = 3499.547610922 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3500.388889' to each side of the equation. -3500.388889 + 3500.388889 + p = 3499.547610922 + 3500.388889 Combine like terms: -3500.388889 + 3500.388889 = 0.000000 0.000000 + p = 3499.547610922 + 3500.388889 p = 3499.547610922 + 3500.388889 Combine like terms: 3499.547610922 + 3500.388889 = 6999.936499922 p = 6999.936499922 Simplifying p = 6999.936499922Subproblem 2
p + -3500.388889 = -3499.547610922 Simplifying p + -3500.388889 = -3499.547610922 Reorder the terms: -3500.388889 + p = -3499.547610922 Solving -3500.388889 + p = -3499.547610922 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3500.388889' to each side of the equation. -3500.388889 + 3500.388889 + p = -3499.547610922 + 3500.388889 Combine like terms: -3500.388889 + 3500.388889 = 0.000000 0.000000 + p = -3499.547610922 + 3500.388889 p = -3499.547610922 + 3500.388889 Combine like terms: -3499.547610922 + 3500.388889 = 0.841278078 p = 0.841278078 Simplifying p = 0.841278078Solution
The solution to the problem is based on the solutions from the subproblems. p = {6999.936499922, 0.841278078}
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