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Simplifying q = 4 + 2q2 Solving q = 4 + 2q2 Solving for variable 'q'. Reorder the terms: -4 + q + -2q2 = 4 + 2q2 + -4 + -2q2 Reorder the terms: -4 + q + -2q2 = 4 + -4 + 2q2 + -2q2 Combine like terms: 4 + -4 = 0 -4 + q + -2q2 = 0 + 2q2 + -2q2 -4 + q + -2q2 = 2q2 + -2q2 Combine like terms: 2q2 + -2q2 = 0 -4 + q + -2q2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2 + -0.5q + q2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.5q + -2 + q2 = 0 + -2 Reorder the terms: 2 + -2 + -0.5q + q2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.5q + q2 = 0 + -2 -0.5q + q2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.5q + q2 = -2 The q term is q. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5q + 0.25 + q2 = -2 + 0.25 Reorder the terms: 0.25 + -0.5q + q2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + -0.5q + q2 = -1.75 Factor a perfect square on the left side: (q + 0.5)(q + 0.5) = -1.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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