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Simplifying 12 + q(5 + -1q) = 0 12 + (5 * q + -1q * q) = 0 12 + (5q + -1q2) = 0 Solving 12 + 5q + -1q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + -5q + q2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -5q + 12 + q2 = 0 + 12 Reorder the terms: -12 + 12 + -5q + q2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -5q + q2 = 0 + 12 -5q + q2 = 0 + 12 Combine like terms: 0 + 12 = 12 -5q + q2 = 12 The q term is -5q. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5q + 6.25 + q2 = 12 + 6.25 Reorder the terms: 6.25 + -5q + q2 = 12 + 6.25 Combine like terms: 12 + 6.25 = 18.25 6.25 + -5q + q2 = 18.25 Factor a perfect square on the left side: (q + -2.5)(q + -2.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (q + -2.5) equal to 4.272001873 and -4.272001873.Subproblem 1
q + -2.5 = 4.272001873 Simplifying q + -2.5 = 4.272001873 Reorder the terms: -2.5 + q = 4.272001873 Solving -2.5 + q = 4.272001873 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + q = 4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + q = 4.272001873 + 2.5 q = 4.272001873 + 2.5 Combine like terms: 4.272001873 + 2.5 = 6.772001873 q = 6.772001873 Simplifying q = 6.772001873Subproblem 2
q + -2.5 = -4.272001873 Simplifying q + -2.5 = -4.272001873 Reorder the terms: -2.5 + q = -4.272001873 Solving -2.5 + q = -4.272001873 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + q = -4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + q = -4.272001873 + 2.5 q = -4.272001873 + 2.5 Combine like terms: -4.272001873 + 2.5 = -1.772001873 q = -1.772001873 Simplifying q = -1.772001873Solution
The solution to the problem is based on the solutions from the subproblems. q = {6.772001873, -1.772001873}
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