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Simplifying 49 + 5q + q2 = 5 + 2q Solving 49 + 5q + q2 = 5 + 2q Solving for variable 'q'. Reorder the terms: 49 + -5 + 5q + -2q + q2 = 5 + 2q + -5 + -2q Combine like terms: 49 + -5 = 44 44 + 5q + -2q + q2 = 5 + 2q + -5 + -2q Combine like terms: 5q + -2q = 3q 44 + 3q + q2 = 5 + 2q + -5 + -2q Reorder the terms: 44 + 3q + q2 = 5 + -5 + 2q + -2q Combine like terms: 5 + -5 = 0 44 + 3q + q2 = 0 + 2q + -2q 44 + 3q + q2 = 2q + -2q Combine like terms: 2q + -2q = 0 44 + 3q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + 3q + -44 + q2 = 0 + -44 Reorder the terms: 44 + -44 + 3q + q2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + 3q + q2 = 0 + -44 3q + q2 = 0 + -44 Combine like terms: 0 + -44 = -44 3q + q2 = -44 The q term is 3q. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3q + 2.25 + q2 = -44 + 2.25 Reorder the terms: 2.25 + 3q + q2 = -44 + 2.25 Combine like terms: -44 + 2.25 = -41.75 2.25 + 3q + q2 = -41.75 Factor a perfect square on the left side: (q + 1.5)(q + 1.5) = -41.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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