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Simplifying 34 + -1.6666q + -0.3333q2 + -2q2 + 3q + 71 = 0 Reorder the terms: 34 + 71 + -1.6666q + 3q + -0.3333q2 + -2q2 = 0 Combine like terms: 34 + 71 = 105 105 + -1.6666q + 3q + -0.3333q2 + -2q2 = 0 Combine like terms: -1.6666q + 3q = 1.3334q 105 + 1.3334q + -0.3333q2 + -2q2 = 0 Combine like terms: -0.3333q2 + -2q2 = -2.3333q2 105 + 1.3334q + -2.3333q2 = 0 Solving 105 + 1.3334q + -2.3333q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -2.3333 the coefficient of the squared term: Divide each side by '-2.3333'. -45.00064287 + -0.5714653066q + q2 = 0 Move the constant term to the right: Add '45.00064287' to each side of the equation. -45.00064287 + -0.5714653066q + 45.00064287 + q2 = 0 + 45.00064287 Reorder the terms: -45.00064287 + 45.00064287 + -0.5714653066q + q2 = 0 + 45.00064287 Combine like terms: -45.00064287 + 45.00064287 = 0.00000000 0.00000000 + -0.5714653066q + q2 = 0 + 45.00064287 -0.5714653066q + q2 = 0 + 45.00064287 Combine like terms: 0 + 45.00064287 = 45.00064287 -0.5714653066q + q2 = 45.00064287 The q term is -0.5714653066q. Take half its coefficient (-0.2857326533). Square it (0.08164314916) and add it to both sides. Add '0.08164314916' to each side of the equation. -0.5714653066q + 0.08164314916 + q2 = 45.00064287 + 0.08164314916 Reorder the terms: 0.08164314916 + -0.5714653066q + q2 = 45.00064287 + 0.08164314916 Combine like terms: 45.00064287 + 0.08164314916 = 45.08228601916 0.08164314916 + -0.5714653066q + q2 = 45.08228601916 Factor a perfect square on the left side: (q + -0.2857326533)(q + -0.2857326533) = 45.08228601916 Calculate the square root of the right side: 6.714334369 Break this problem into two subproblems by setting (q + -0.2857326533) equal to 6.714334369 and -6.714334369.Subproblem 1
q + -0.2857326533 = 6.714334369 Simplifying q + -0.2857326533 = 6.714334369 Reorder the terms: -0.2857326533 + q = 6.714334369 Solving -0.2857326533 + q = 6.714334369 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.2857326533' to each side of the equation. -0.2857326533 + 0.2857326533 + q = 6.714334369 + 0.2857326533 Combine like terms: -0.2857326533 + 0.2857326533 = 0.0000000000 0.0000000000 + q = 6.714334369 + 0.2857326533 q = 6.714334369 + 0.2857326533 Combine like terms: 6.714334369 + 0.2857326533 = 7.0000670223 q = 7.0000670223 Simplifying q = 7.0000670223Subproblem 2
q + -0.2857326533 = -6.714334369 Simplifying q + -0.2857326533 = -6.714334369 Reorder the terms: -0.2857326533 + q = -6.714334369 Solving -0.2857326533 + q = -6.714334369 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.2857326533' to each side of the equation. -0.2857326533 + 0.2857326533 + q = -6.714334369 + 0.2857326533 Combine like terms: -0.2857326533 + 0.2857326533 = 0.0000000000 0.0000000000 + q = -6.714334369 + 0.2857326533 q = -6.714334369 + 0.2857326533 Combine like terms: -6.714334369 + 0.2857326533 = -6.4286017157 q = -6.4286017157 Simplifying q = -6.4286017157Solution
The solution to the problem is based on the solutions from the subproblems. q = {7.0000670223, -6.4286017157}
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