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Simplifying (1250q + -8q2) + -1(125 + 6q2) = 0 Remove parenthesis around (1250q + -8q2) 1250q + -8q2 + -1(125 + 6q2) = 0 1250q + -8q2 + (125 * -1 + 6q2 * -1) = 0 1250q + -8q2 + (-125 + -6q2) = 0 Reorder the terms: -125 + 1250q + -8q2 + -6q2 = 0 Combine like terms: -8q2 + -6q2 = -14q2 -125 + 1250q + -14q2 = 0 Solving -125 + 1250q + -14q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. 8.928571429 + -89.28571429q + q2 = 0 Move the constant term to the right: Add '-8.928571429' to each side of the equation. 8.928571429 + -89.28571429q + -8.928571429 + q2 = 0 + -8.928571429 Reorder the terms: 8.928571429 + -8.928571429 + -89.28571429q + q2 = 0 + -8.928571429 Combine like terms: 8.928571429 + -8.928571429 = 0.000000000 0.000000000 + -89.28571429q + q2 = 0 + -8.928571429 -89.28571429q + q2 = 0 + -8.928571429 Combine like terms: 0 + -8.928571429 = -8.928571429 -89.28571429q + q2 = -8.928571429 The q term is -89.28571429q. Take half its coefficient (-44.64285715). Square it (1992.984695) and add it to both sides. Add '1992.984695' to each side of the equation. -89.28571429q + 1992.984695 + q2 = -8.928571429 + 1992.984695 Reorder the terms: 1992.984695 + -89.28571429q + q2 = -8.928571429 + 1992.984695 Combine like terms: -8.928571429 + 1992.984695 = 1984.056123571 1992.984695 + -89.28571429q + q2 = 1984.056123571 Factor a perfect square on the left side: (q + -44.64285715)(q + -44.64285715) = 1984.056123571 Calculate the square root of the right side: 44.542744904 Break this problem into two subproblems by setting (q + -44.64285715) equal to 44.542744904 and -44.542744904.Subproblem 1
q + -44.64285715 = 44.542744904 Simplifying q + -44.64285715 = 44.542744904 Reorder the terms: -44.64285715 + q = 44.542744904 Solving -44.64285715 + q = 44.542744904 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '44.64285715' to each side of the equation. -44.64285715 + 44.64285715 + q = 44.542744904 + 44.64285715 Combine like terms: -44.64285715 + 44.64285715 = 0.00000000 0.00000000 + q = 44.542744904 + 44.64285715 q = 44.542744904 + 44.64285715 Combine like terms: 44.542744904 + 44.64285715 = 89.185602054 q = 89.185602054 Simplifying q = 89.185602054Subproblem 2
q + -44.64285715 = -44.542744904 Simplifying q + -44.64285715 = -44.542744904 Reorder the terms: -44.64285715 + q = -44.542744904 Solving -44.64285715 + q = -44.542744904 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '44.64285715' to each side of the equation. -44.64285715 + 44.64285715 + q = -44.542744904 + 44.64285715 Combine like terms: -44.64285715 + 44.64285715 = 0.00000000 0.00000000 + q = -44.542744904 + 44.64285715 q = -44.542744904 + 44.64285715 Combine like terms: -44.542744904 + 44.64285715 = 0.100112246 q = 0.100112246 Simplifying q = 0.100112246Solution
The solution to the problem is based on the solutions from the subproblems. q = {89.185602054, 0.100112246}
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