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Simplifying q2 + 4q + 4 = 26 Reorder the terms: 4 + 4q + q2 = 26 Solving 4 + 4q + q2 = 26 Solving for variable 'q'. Reorder the terms: 4 + -26 + 4q + q2 = 26 + -26 Combine like terms: 4 + -26 = -22 -22 + 4q + q2 = 26 + -26 Combine like terms: 26 + -26 = 0 -22 + 4q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 4q + 22 + q2 = 0 + 22 Reorder the terms: -22 + 22 + 4q + q2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 4q + q2 = 0 + 22 4q + q2 = 0 + 22 Combine like terms: 0 + 22 = 22 4q + q2 = 22 The q term is 4q. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4q + 4 + q2 = 22 + 4 Reorder the terms: 4 + 4q + q2 = 22 + 4 Combine like terms: 22 + 4 = 26 4 + 4q + q2 = 26 Factor a perfect square on the left side: (q + 2)(q + 2) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (q + 2) equal to 5.099019514 and -5.099019514.Subproblem 1
q + 2 = 5.099019514 Simplifying q + 2 = 5.099019514 Reorder the terms: 2 + q = 5.099019514 Solving 2 + q = 5.099019514 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + q = 5.099019514 + -2 Combine like terms: 2 + -2 = 0 0 + q = 5.099019514 + -2 q = 5.099019514 + -2 Combine like terms: 5.099019514 + -2 = 3.099019514 q = 3.099019514 Simplifying q = 3.099019514Subproblem 2
q + 2 = -5.099019514 Simplifying q + 2 = -5.099019514 Reorder the terms: 2 + q = -5.099019514 Solving 2 + q = -5.099019514 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + q = -5.099019514 + -2 Combine like terms: 2 + -2 = 0 0 + q = -5.099019514 + -2 q = -5.099019514 + -2 Combine like terms: -5.099019514 + -2 = -7.099019514 q = -7.099019514 Simplifying q = -7.099019514Solution
The solution to the problem is based on the solutions from the subproblems. q = {3.099019514, -7.099019514}
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