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Simplifying 320 = 0 + 4q + 9q2 Remove the zero: 320 = 4q + 9q2 Solving 320 = 4q + 9q2 Solving for variable 'q'. Reorder the terms: 320 + -4q + -9q2 = 4q + -4q + 9q2 + -9q2 Combine like terms: 4q + -4q = 0 320 + -4q + -9q2 = 0 + 9q2 + -9q2 320 + -4q + -9q2 = 9q2 + -9q2 Combine like terms: 9q2 + -9q2 = 0 320 + -4q + -9q2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -35.55555556 + 0.4444444444q + q2 = 0 Move the constant term to the right: Add '35.55555556' to each side of the equation. -35.55555556 + 0.4444444444q + 35.55555556 + q2 = 0 + 35.55555556 Reorder the terms: -35.55555556 + 35.55555556 + 0.4444444444q + q2 = 0 + 35.55555556 Combine like terms: -35.55555556 + 35.55555556 = 0.00000000 0.00000000 + 0.4444444444q + q2 = 0 + 35.55555556 0.4444444444q + q2 = 0 + 35.55555556 Combine like terms: 0 + 35.55555556 = 35.55555556 0.4444444444q + q2 = 35.55555556 The q term is 0.4444444444q. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444q + 0.04938271604 + q2 = 35.55555556 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444q + q2 = 35.55555556 + 0.04938271604 Combine like terms: 35.55555556 + 0.04938271604 = 35.60493827604 0.04938271604 + 0.4444444444q + q2 = 35.60493827604 Factor a perfect square on the left side: (q + 0.2222222222)(q + 0.2222222222) = 35.60493827604 Calculate the square root of the right side: 5.96698737 Break this problem into two subproblems by setting (q + 0.2222222222) equal to 5.96698737 and -5.96698737.Subproblem 1
q + 0.2222222222 = 5.96698737 Simplifying q + 0.2222222222 = 5.96698737 Reorder the terms: 0.2222222222 + q = 5.96698737 Solving 0.2222222222 + q = 5.96698737 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + q = 5.96698737 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + q = 5.96698737 + -0.2222222222 q = 5.96698737 + -0.2222222222 Combine like terms: 5.96698737 + -0.2222222222 = 5.7447651478 q = 5.7447651478 Simplifying q = 5.7447651478Subproblem 2
q + 0.2222222222 = -5.96698737 Simplifying q + 0.2222222222 = -5.96698737 Reorder the terms: 0.2222222222 + q = -5.96698737 Solving 0.2222222222 + q = -5.96698737 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + q = -5.96698737 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + q = -5.96698737 + -0.2222222222 q = -5.96698737 + -0.2222222222 Combine like terms: -5.96698737 + -0.2222222222 = -6.1892095922 q = -6.1892095922 Simplifying q = -6.1892095922Solution
The solution to the problem is based on the solutions from the subproblems. q = {5.7447651478, -6.1892095922}
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