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Simplifying -5q2 + 35q + -26 = 0 Reorder the terms: -26 + 35q + -5q2 = 0 Solving -26 + 35q + -5q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 5.2 + -7q + q2 = 0 Move the constant term to the right: Add '-5.2' to each side of the equation. 5.2 + -7q + -5.2 + q2 = 0 + -5.2 Reorder the terms: 5.2 + -5.2 + -7q + q2 = 0 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + -7q + q2 = 0 + -5.2 -7q + q2 = 0 + -5.2 Combine like terms: 0 + -5.2 = -5.2 -7q + q2 = -5.2 The q term is -7q. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7q + 12.25 + q2 = -5.2 + 12.25 Reorder the terms: 12.25 + -7q + q2 = -5.2 + 12.25 Combine like terms: -5.2 + 12.25 = 7.05 12.25 + -7q + q2 = 7.05 Factor a perfect square on the left side: (q + -3.5)(q + -3.5) = 7.05 Calculate the square root of the right side: 2.655183609 Break this problem into two subproblems by setting (q + -3.5) equal to 2.655183609 and -2.655183609.Subproblem 1
q + -3.5 = 2.655183609 Simplifying q + -3.5 = 2.655183609 Reorder the terms: -3.5 + q = 2.655183609 Solving -3.5 + q = 2.655183609 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + q = 2.655183609 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + q = 2.655183609 + 3.5 q = 2.655183609 + 3.5 Combine like terms: 2.655183609 + 3.5 = 6.155183609 q = 6.155183609 Simplifying q = 6.155183609Subproblem 2
q + -3.5 = -2.655183609 Simplifying q + -3.5 = -2.655183609 Reorder the terms: -3.5 + q = -2.655183609 Solving -3.5 + q = -2.655183609 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + q = -2.655183609 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + q = -2.655183609 + 3.5 q = -2.655183609 + 3.5 Combine like terms: -2.655183609 + 3.5 = 0.844816391 q = 0.844816391 Simplifying q = 0.844816391Solution
The solution to the problem is based on the solutions from the subproblems. q = {6.155183609, 0.844816391}
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