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Simplifying q2 + 22q = 25 Reorder the terms: 22q + q2 = 25 Solving 22q + q2 = 25 Solving for variable 'q'. Reorder the terms: -25 + 22q + q2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 22q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 22q + 25 + q2 = 0 + 25 Reorder the terms: -25 + 25 + 22q + q2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 22q + q2 = 0 + 25 22q + q2 = 0 + 25 Combine like terms: 0 + 25 = 25 22q + q2 = 25 The q term is 22q. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22q + 121 + q2 = 25 + 121 Reorder the terms: 121 + 22q + q2 = 25 + 121 Combine like terms: 25 + 121 = 146 121 + 22q + q2 = 146 Factor a perfect square on the left side: (q + 11)(q + 11) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (q + 11) equal to 12.083045974 and -12.083045974.Subproblem 1
q + 11 = 12.083045974 Simplifying q + 11 = 12.083045974 Reorder the terms: 11 + q = 12.083045974 Solving 11 + q = 12.083045974 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + q = 12.083045974 + -11 Combine like terms: 11 + -11 = 0 0 + q = 12.083045974 + -11 q = 12.083045974 + -11 Combine like terms: 12.083045974 + -11 = 1.083045974 q = 1.083045974 Simplifying q = 1.083045974Subproblem 2
q + 11 = -12.083045974 Simplifying q + 11 = -12.083045974 Reorder the terms: 11 + q = -12.083045974 Solving 11 + q = -12.083045974 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + q = -12.083045974 + -11 Combine like terms: 11 + -11 = 0 0 + q = -12.083045974 + -11 q = -12.083045974 + -11 Combine like terms: -12.083045974 + -11 = -23.083045974 q = -23.083045974 Simplifying q = -23.083045974Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.083045974, -23.083045974}
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