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Simplifying (q2 + 6q) + (4q + 1) = 0 Reorder the terms: (6q + q2) + (4q + 1) = 0 Remove parenthesis around (6q + q2) 6q + q2 + (4q + 1) = 0 Reorder the terms: 6q + q2 + (1 + 4q) = 0 Remove parenthesis around (1 + 4q) 6q + q2 + 1 + 4q = 0 Reorder the terms: 1 + 6q + 4q + q2 = 0 Combine like terms: 6q + 4q = 10q 1 + 10q + q2 = 0 Solving 1 + 10q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 10q + -1 + q2 = 0 + -1 Reorder the terms: 1 + -1 + 10q + q2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 10q + q2 = 0 + -1 10q + q2 = 0 + -1 Combine like terms: 0 + -1 = -1 10q + q2 = -1 The q term is 10q. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10q + 25 + q2 = -1 + 25 Reorder the terms: 25 + 10q + q2 = -1 + 25 Combine like terms: -1 + 25 = 24 25 + 10q + q2 = 24 Factor a perfect square on the left side: (q + 5)(q + 5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (q + 5) equal to 4.898979486 and -4.898979486.Subproblem 1
q + 5 = 4.898979486 Simplifying q + 5 = 4.898979486 Reorder the terms: 5 + q = 4.898979486 Solving 5 + q = 4.898979486 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + q = 4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + q = 4.898979486 + -5 q = 4.898979486 + -5 Combine like terms: 4.898979486 + -5 = -0.101020514 q = -0.101020514 Simplifying q = -0.101020514Subproblem 2
q + 5 = -4.898979486 Simplifying q + 5 = -4.898979486 Reorder the terms: 5 + q = -4.898979486 Solving 5 + q = -4.898979486 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + q = -4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + q = -4.898979486 + -5 q = -4.898979486 + -5 Combine like terms: -4.898979486 + -5 = -9.898979486 q = -9.898979486 Simplifying q = -9.898979486Solution
The solution to the problem is based on the solutions from the subproblems. q = {-0.101020514, -9.898979486}
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