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Simplifying 16 + -16q + 2.25q2 = 0 Solving 16 + -16q + 2.25q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 2.25 the coefficient of the squared term: Divide each side by '2.25'. 7.111111111 + -7.111111111q + q2 = 0 Move the constant term to the right: Add '-7.111111111' to each side of the equation. 7.111111111 + -7.111111111q + -7.111111111 + q2 = 0 + -7.111111111 Reorder the terms: 7.111111111 + -7.111111111 + -7.111111111q + q2 = 0 + -7.111111111 Combine like terms: 7.111111111 + -7.111111111 = 0.000000000 0.000000000 + -7.111111111q + q2 = 0 + -7.111111111 -7.111111111q + q2 = 0 + -7.111111111 Combine like terms: 0 + -7.111111111 = -7.111111111 -7.111111111q + q2 = -7.111111111 The q term is -7.111111111q. Take half its coefficient (-3.555555556). Square it (12.64197531) and add it to both sides. Add '12.64197531' to each side of the equation. -7.111111111q + 12.64197531 + q2 = -7.111111111 + 12.64197531 Reorder the terms: 12.64197531 + -7.111111111q + q2 = -7.111111111 + 12.64197531 Combine like terms: -7.111111111 + 12.64197531 = 5.530864199 12.64197531 + -7.111111111q + q2 = 5.530864199 Factor a perfect square on the left side: (q + -3.555555556)(q + -3.555555556) = 5.530864199 Calculate the square root of the right side: 2.351778943 Break this problem into two subproblems by setting (q + -3.555555556) equal to 2.351778943 and -2.351778943.Subproblem 1
q + -3.555555556 = 2.351778943 Simplifying q + -3.555555556 = 2.351778943 Reorder the terms: -3.555555556 + q = 2.351778943 Solving -3.555555556 + q = 2.351778943 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + q = 2.351778943 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + q = 2.351778943 + 3.555555556 q = 2.351778943 + 3.555555556 Combine like terms: 2.351778943 + 3.555555556 = 5.907334499 q = 5.907334499 Simplifying q = 5.907334499Subproblem 2
q + -3.555555556 = -2.351778943 Simplifying q + -3.555555556 = -2.351778943 Reorder the terms: -3.555555556 + q = -2.351778943 Solving -3.555555556 + q = -2.351778943 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + q = -2.351778943 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + q = -2.351778943 + 3.555555556 q = -2.351778943 + 3.555555556 Combine like terms: -2.351778943 + 3.555555556 = 1.203776613 q = 1.203776613 Simplifying q = 1.203776613Solution
The solution to the problem is based on the solutions from the subproblems. q = {5.907334499, 1.203776613}
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