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Simplifying 0 = -0.02q2 + 3q + -41 Reorder the terms: 0 = -41 + 3q + -0.02q2 Solving 0 = -41 + 3q + -0.02q2 Solving for variable 'q'. Combine like terms: 0 + 41 = 41 41 + -3q + 0.02q2 = -41 + 3q + -0.02q2 + 41 + -3q + 0.02q2 Reorder the terms: 41 + -3q + 0.02q2 = -41 + 41 + 3q + -3q + -0.02q2 + 0.02q2 Combine like terms: -41 + 41 = 0 41 + -3q + 0.02q2 = 0 + 3q + -3q + -0.02q2 + 0.02q2 41 + -3q + 0.02q2 = 3q + -3q + -0.02q2 + 0.02q2 Combine like terms: 3q + -3q = 0 41 + -3q + 0.02q2 = 0 + -0.02q2 + 0.02q2 41 + -3q + 0.02q2 = -0.02q2 + 0.02q2 Combine like terms: -0.02q2 + 0.02q2 = 0.00 41 + -3q + 0.02q2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 2050 + -150q + q2 = 0 Move the constant term to the right: Add '-2050' to each side of the equation. 2050 + -150q + -2050 + q2 = 0 + -2050 Reorder the terms: 2050 + -2050 + -150q + q2 = 0 + -2050 Combine like terms: 2050 + -2050 = 0 0 + -150q + q2 = 0 + -2050 -150q + q2 = 0 + -2050 Combine like terms: 0 + -2050 = -2050 -150q + q2 = -2050 The q term is -150q. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150q + 5625 + q2 = -2050 + 5625 Reorder the terms: 5625 + -150q + q2 = -2050 + 5625 Combine like terms: -2050 + 5625 = 3575 5625 + -150q + q2 = 3575 Factor a perfect square on the left side: (q + -75)(q + -75) = 3575 Calculate the square root of the right side: 59.791303716 Break this problem into two subproblems by setting (q + -75) equal to 59.791303716 and -59.791303716.Subproblem 1
q + -75 = 59.791303716 Simplifying q + -75 = 59.791303716 Reorder the terms: -75 + q = 59.791303716 Solving -75 + q = 59.791303716 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + q = 59.791303716 + 75 Combine like terms: -75 + 75 = 0 0 + q = 59.791303716 + 75 q = 59.791303716 + 75 Combine like terms: 59.791303716 + 75 = 134.791303716 q = 134.791303716 Simplifying q = 134.791303716Subproblem 2
q + -75 = -59.791303716 Simplifying q + -75 = -59.791303716 Reorder the terms: -75 + q = -59.791303716 Solving -75 + q = -59.791303716 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + q = -59.791303716 + 75 Combine like terms: -75 + 75 = 0 0 + q = -59.791303716 + 75 q = -59.791303716 + 75 Combine like terms: -59.791303716 + 75 = 15.208696284 q = 15.208696284 Simplifying q = 15.208696284Solution
The solution to the problem is based on the solutions from the subproblems. q = {134.791303716, 15.208696284}
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