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Simplifying 8q2 + -21 = 7q2 + -4q + 15 Reorder the terms: -21 + 8q2 = 7q2 + -4q + 15 Reorder the terms: -21 + 8q2 = 15 + -4q + 7q2 Solving -21 + 8q2 = 15 + -4q + 7q2 Solving for variable 'q'. Reorder the terms: -21 + -15 + 4q + 8q2 + -7q2 = 15 + -4q + 7q2 + -15 + 4q + -7q2 Combine like terms: -21 + -15 = -36 -36 + 4q + 8q2 + -7q2 = 15 + -4q + 7q2 + -15 + 4q + -7q2 Combine like terms: 8q2 + -7q2 = 1q2 -36 + 4q + 1q2 = 15 + -4q + 7q2 + -15 + 4q + -7q2 Reorder the terms: -36 + 4q + 1q2 = 15 + -15 + -4q + 4q + 7q2 + -7q2 Combine like terms: 15 + -15 = 0 -36 + 4q + 1q2 = 0 + -4q + 4q + 7q2 + -7q2 -36 + 4q + 1q2 = -4q + 4q + 7q2 + -7q2 Combine like terms: -4q + 4q = 0 -36 + 4q + 1q2 = 0 + 7q2 + -7q2 -36 + 4q + 1q2 = 7q2 + -7q2 Combine like terms: 7q2 + -7q2 = 0 -36 + 4q + 1q2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 4q + 36 + q2 = 0 + 36 Reorder the terms: -36 + 36 + 4q + q2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 4q + q2 = 0 + 36 4q + q2 = 0 + 36 Combine like terms: 0 + 36 = 36 4q + q2 = 36 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 = 36 + 4 Reorder the terms: 4 + 4q + q2 = 36 + 4 Combine like terms: 36 + 4 = 40 4 + 4q + q2 = 40 Factor a perfect square on the left side: (q + 2)(q + 2) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (q + 2) equal to 6.32455532 and -6.32455532.Subproblem 1
q + 2 = 6.32455532 Simplifying q + 2 = 6.32455532 Reorder the terms: 2 + q = 6.32455532 Solving 2 + q = 6.32455532 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 = 6.32455532 + -2 Combine like terms: 2 + -2 = 0 0 + q = 6.32455532 + -2 q = 6.32455532 + -2 Combine like terms: 6.32455532 + -2 = 4.32455532 q = 4.32455532 Simplifying q = 4.32455532Subproblem 2
q + 2 = -6.32455532 Simplifying q + 2 = -6.32455532 Reorder the terms: 2 + q = -6.32455532 Solving 2 + q = -6.32455532 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 = -6.32455532 + -2 Combine like terms: 2 + -2 = 0 0 + q = -6.32455532 + -2 q = -6.32455532 + -2 Combine like terms: -6.32455532 + -2 = -8.32455532 q = -8.32455532 Simplifying q = -8.32455532Solution
The solution to the problem is based on the solutions from the subproblems. q = {4.32455532, -8.32455532}
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