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Simplifying 4q2 + -3q = 3q2 + -4q + 18 Reorder the terms: -3q + 4q2 = 3q2 + -4q + 18 Reorder the terms: -3q + 4q2 = 18 + -4q + 3q2 Solving -3q + 4q2 = 18 + -4q + 3q2 Solving for variable 'q'. Reorder the terms: -18 + -3q + 4q + 4q2 + -3q2 = 18 + -4q + 3q2 + -18 + 4q + -3q2 Combine like terms: -3q + 4q = 1q -18 + 1q + 4q2 + -3q2 = 18 + -4q + 3q2 + -18 + 4q + -3q2 Combine like terms: 4q2 + -3q2 = 1q2 -18 + 1q + 1q2 = 18 + -4q + 3q2 + -18 + 4q + -3q2 Reorder the terms: -18 + 1q + 1q2 = 18 + -18 + -4q + 4q + 3q2 + -3q2 Combine like terms: 18 + -18 = 0 -18 + 1q + 1q2 = 0 + -4q + 4q + 3q2 + -3q2 -18 + 1q + 1q2 = -4q + 4q + 3q2 + -3q2 Combine like terms: -4q + 4q = 0 -18 + 1q + 1q2 = 0 + 3q2 + -3q2 -18 + 1q + 1q2 = 3q2 + -3q2 Combine like terms: 3q2 + -3q2 = 0 -18 + 1q + 1q2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 1q + 18 + q2 = 0 + 18 Reorder the terms: -18 + 18 + 1q + q2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 1q + q2 = 0 + 18 1q + q2 = 0 + 18 Combine like terms: 0 + 18 = 18 1q + q2 = 18 The q term is 1q. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. q + 0.25 + q2 = 18 + 0.25 Reorder the terms: 0.25 + q + q2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + q + q2 = 18.25 Factor a perfect square on the left side: (q + 0.5)(q + 0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (q + 0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
q + 0.5 = 4.272001873 Simplifying q + 0.5 = 4.272001873 Reorder the terms: 0.5 + q = 4.272001873 Solving 0.5 + q = 4.272001873 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q = 4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = 4.272001873 + -0.5 q = 4.272001873 + -0.5 Combine like terms: 4.272001873 + -0.5 = 3.772001873 q = 3.772001873 Simplifying q = 3.772001873Subproblem 2
q + 0.5 = -4.272001873 Simplifying q + 0.5 = -4.272001873 Reorder the terms: 0.5 + q = -4.272001873 Solving 0.5 + q = -4.272001873 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q = -4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = -4.272001873 + -0.5 q = -4.272001873 + -0.5 Combine like terms: -4.272001873 + -0.5 = -4.772001873 q = -4.772001873 Simplifying q = -4.772001873Solution
The solution to the problem is based on the solutions from the subproblems. q = {3.772001873, -4.772001873}
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