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Simplifying q2 + -22q = -5 Reorder the terms: -22q + q2 = -5 Solving -22q + q2 = -5 Solving for variable 'q'. Reorder the terms: 5 + -22q + q2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + -22q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -22q + -5 + q2 = 0 + -5 Reorder the terms: 5 + -5 + -22q + q2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -22q + q2 = 0 + -5 -22q + q2 = 0 + -5 Combine like terms: 0 + -5 = -5 -22q + q2 = -5 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 = -5 + 121 Reorder the terms: 121 + -22q + q2 = -5 + 121 Combine like terms: -5 + 121 = 116 121 + -22q + q2 = 116 Factor a perfect square on the left side: (q + -11)(q + -11) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (q + -11) equal to 10.770329614 and -10.770329614.Subproblem 1
q + -11 = 10.770329614 Simplifying q + -11 = 10.770329614 Reorder the terms: -11 + q = 10.770329614 Solving -11 + q = 10.770329614 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 = 10.770329614 + 11 Combine like terms: -11 + 11 = 0 0 + q = 10.770329614 + 11 q = 10.770329614 + 11 Combine like terms: 10.770329614 + 11 = 21.770329614 q = 21.770329614 Simplifying q = 21.770329614Subproblem 2
q + -11 = -10.770329614 Simplifying q + -11 = -10.770329614 Reorder the terms: -11 + q = -10.770329614 Solving -11 + q = -10.770329614 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 = -10.770329614 + 11 Combine like terms: -11 + 11 = 0 0 + q = -10.770329614 + 11 q = -10.770329614 + 11 Combine like terms: -10.770329614 + 11 = 0.229670386 q = 0.229670386 Simplifying q = 0.229670386Solution
The solution to the problem is based on the solutions from the subproblems. q = {21.770329614, 0.229670386}
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