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Simplifying 8q2 + -6q = 7q2 + -8q + 25 Reorder the terms: -6q + 8q2 = 7q2 + -8q + 25 Reorder the terms: -6q + 8q2 = 25 + -8q + 7q2 Solving -6q + 8q2 = 25 + -8q + 7q2 Solving for variable 'q'. Reorder the terms: -25 + -6q + 8q + 8q2 + -7q2 = 25 + -8q + 7q2 + -25 + 8q + -7q2 Combine like terms: -6q + 8q = 2q -25 + 2q + 8q2 + -7q2 = 25 + -8q + 7q2 + -25 + 8q + -7q2 Combine like terms: 8q2 + -7q2 = 1q2 -25 + 2q + 1q2 = 25 + -8q + 7q2 + -25 + 8q + -7q2 Reorder the terms: -25 + 2q + 1q2 = 25 + -25 + -8q + 8q + 7q2 + -7q2 Combine like terms: 25 + -25 = 0 -25 + 2q + 1q2 = 0 + -8q + 8q + 7q2 + -7q2 -25 + 2q + 1q2 = -8q + 8q + 7q2 + -7q2 Combine like terms: -8q + 8q = 0 -25 + 2q + 1q2 = 0 + 7q2 + -7q2 -25 + 2q + 1q2 = 7q2 + -7q2 Combine like terms: 7q2 + -7q2 = 0 -25 + 2q + 1q2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 2q + 25 + q2 = 0 + 25 Reorder the terms: -25 + 25 + 2q + q2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2q + q2 = 0 + 25 2q + q2 = 0 + 25 Combine like terms: 0 + 25 = 25 2q + q2 = 25 The q term is 2q. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2q + 1 + q2 = 25 + 1 Reorder the terms: 1 + 2q + q2 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + 2q + q2 = 26 Factor a perfect square on the left side: (q + 1)(q + 1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (q + 1) equal to 5.099019514 and -5.099019514.Subproblem 1
q + 1 = 5.099019514 Simplifying q + 1 = 5.099019514 Reorder the terms: 1 + q = 5.099019514 Solving 1 + q = 5.099019514 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = 5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + q = 5.099019514 + -1 q = 5.099019514 + -1 Combine like terms: 5.099019514 + -1 = 4.099019514 q = 4.099019514 Simplifying q = 4.099019514Subproblem 2
q + 1 = -5.099019514 Simplifying q + 1 = -5.099019514 Reorder the terms: 1 + q = -5.099019514 Solving 1 + q = -5.099019514 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = -5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + q = -5.099019514 + -1 q = -5.099019514 + -1 Combine like terms: -5.099019514 + -1 = -6.099019514 q = -6.099019514 Simplifying q = -6.099019514Solution
The solution to the problem is based on the solutions from the subproblems. q = {4.099019514, -6.099019514}
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