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Simplifying 1000q + -1q2 = 80 Solving 1000q + -1q2 = 80 Solving for variable 'q'. Reorder the terms: -80 + 1000q + -1q2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 1000q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 80 + -1000q + q2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -1000q + -80 + q2 = 0 + -80 Reorder the terms: 80 + -80 + -1000q + q2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -1000q + q2 = 0 + -80 -1000q + q2 = 0 + -80 Combine like terms: 0 + -80 = -80 -1000q + q2 = -80 The q term is -1000q. Take half its coefficient (-500). Square it (250000) and add it to both sides. Add '250000' to each side of the equation. -1000q + 250000 + q2 = -80 + 250000 Reorder the terms: 250000 + -1000q + q2 = -80 + 250000 Combine like terms: -80 + 250000 = 249920 250000 + -1000q + q2 = 249920 Factor a perfect square on the left side: (q + -500)(q + -500) = 249920 Calculate the square root of the right side: 499.919993599 Break this problem into two subproblems by setting (q + -500) equal to 499.919993599 and -499.919993599.Subproblem 1
q + -500 = 499.919993599 Simplifying q + -500 = 499.919993599 Reorder the terms: -500 + q = 499.919993599 Solving -500 + q = 499.919993599 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + q = 499.919993599 + 500 Combine like terms: -500 + 500 = 0 0 + q = 499.919993599 + 500 q = 499.919993599 + 500 Combine like terms: 499.919993599 + 500 = 999.919993599 q = 999.919993599 Simplifying q = 999.919993599Subproblem 2
q + -500 = -499.919993599 Simplifying q + -500 = -499.919993599 Reorder the terms: -500 + q = -499.919993599 Solving -500 + q = -499.919993599 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + q = -499.919993599 + 500 Combine like terms: -500 + 500 = 0 0 + q = -499.919993599 + 500 q = -499.919993599 + 500 Combine like terms: -499.919993599 + 500 = 0.080006401 q = 0.080006401 Simplifying q = 0.080006401Solution
The solution to the problem is based on the solutions from the subproblems. q = {999.919993599, 0.080006401}
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