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Simplifying 2q2 + -12q = -22 Reorder the terms: -12q + 2q2 = -22 Solving -12q + 2q2 = -22 Solving for variable 'q'. Reorder the terms: 22 + -12q + 2q2 = -22 + 22 Combine like terms: -22 + 22 = 0 22 + -12q + 2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -6q + q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -6q + q2)' equal to zero and attempt to solve: Simplifying 11 + -6q + q2 = 0 Solving 11 + -6q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -6q + -11 + q2 = 0 + -11 Reorder the terms: 11 + -11 + -6q + q2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -6q + q2 = 0 + -11 -6q + q2 = 0 + -11 Combine like terms: 0 + -11 = -11 -6q + q2 = -11 The q term is -6q. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6q + 9 + q2 = -11 + 9 Reorder the terms: 9 + -6q + q2 = -11 + 9 Combine like terms: -11 + 9 = -2 9 + -6q + q2 = -2 Factor a perfect square on the left side: (q + -3)(q + -3) = -2 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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