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Simplifying q2 + -4q + 25 = q + 5 Reorder the terms: 25 + -4q + q2 = q + 5 Reorder the terms: 25 + -4q + q2 = 5 + q Solving 25 + -4q + q2 = 5 + q Solving for variable 'q'. Reorder the terms: 25 + -5 + -4q + -1q + q2 = 5 + q + -5 + -1q Combine like terms: 25 + -5 = 20 20 + -4q + -1q + q2 = 5 + q + -5 + -1q Combine like terms: -4q + -1q = -5q 20 + -5q + q2 = 5 + q + -5 + -1q Reorder the terms: 20 + -5q + q2 = 5 + -5 + q + -1q Combine like terms: 5 + -5 = 0 20 + -5q + q2 = 0 + q + -1q 20 + -5q + q2 = q + -1q Combine like terms: q + -1q = 0 20 + -5q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -5q + -20 + q2 = 0 + -20 Reorder the terms: 20 + -20 + -5q + q2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -5q + q2 = 0 + -20 -5q + q2 = 0 + -20 Combine like terms: 0 + -20 = -20 -5q + q2 = -20 The q term is -5q. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5q + 6.25 + q2 = -20 + 6.25 Reorder the terms: 6.25 + -5q + q2 = -20 + 6.25 Combine like terms: -20 + 6.25 = -13.75 6.25 + -5q + q2 = -13.75 Factor a perfect square on the left side: (q + -2.5)(q + -2.5) = -13.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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