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Simplifying 35 + -16q + 2.25q2 = 51 Solving 35 + -16q + 2.25q2 = 51 Solving for variable 'q'. Reorder the terms: 35 + -51 + -16q + 2.25q2 = 51 + -51 Combine like terms: 35 + -51 = -16 -16 + -16q + 2.25q2 = 51 + -51 Combine like terms: 51 + -51 = 0 -16 + -16q + 2.25q2 = 0 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 = 19.753086421 12.64197531 + -7.111111111q + q2 = 19.753086421 Factor a perfect square on the left side: (q + -3.555555556)(q + -3.555555556) = 19.753086421 Calculate the square root of the right side: 4.444444445 Break this problem into two subproblems by setting (q + -3.555555556) equal to 4.444444445 and -4.444444445.Subproblem 1
q + -3.555555556 = 4.444444445 Simplifying q + -3.555555556 = 4.444444445 Reorder the terms: -3.555555556 + q = 4.444444445 Solving -3.555555556 + q = 4.444444445 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 = 4.444444445 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + q = 4.444444445 + 3.555555556 q = 4.444444445 + 3.555555556 Combine like terms: 4.444444445 + 3.555555556 = 8.000000001 q = 8.000000001 Simplifying q = 8.000000001Subproblem 2
q + -3.555555556 = -4.444444445 Simplifying q + -3.555555556 = -4.444444445 Reorder the terms: -3.555555556 + q = -4.444444445 Solving -3.555555556 + q = -4.444444445 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 = -4.444444445 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + q = -4.444444445 + 3.555555556 q = -4.444444445 + 3.555555556 Combine like terms: -4.444444445 + 3.555555556 = -0.888888889 q = -0.888888889 Simplifying q = -0.888888889Solution
The solution to the problem is based on the solutions from the subproblems. q = {8.000000001, -0.888888889}
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