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Simplifying 0.5q + 0.16q = 50 + 0.5q + 0.08q2 Combine like terms: 0.5q + 0.16q = 0.66q 0.66q = 50 + 0.5q + 0.08q2 Solving 0.66q = 50 + 0.5q + 0.08q2 Solving for variable 'q'. Reorder the terms: -50 + 0.66q + -0.5q + -0.08q2 = 50 + 0.5q + 0.08q2 + -50 + -0.5q + -0.08q2 Combine like terms: 0.66q + -0.5q = 0.16q -50 + 0.16q + -0.08q2 = 50 + 0.5q + 0.08q2 + -50 + -0.5q + -0.08q2 Reorder the terms: -50 + 0.16q + -0.08q2 = 50 + -50 + 0.5q + -0.5q + 0.08q2 + -0.08q2 Combine like terms: 50 + -50 = 0 -50 + 0.16q + -0.08q2 = 0 + 0.5q + -0.5q + 0.08q2 + -0.08q2 -50 + 0.16q + -0.08q2 = 0.5q + -0.5q + 0.08q2 + -0.08q2 Combine like terms: 0.5q + -0.5q = 0.0 -50 + 0.16q + -0.08q2 = 0.0 + 0.08q2 + -0.08q2 -50 + 0.16q + -0.08q2 = 0.08q2 + -0.08q2 Combine like terms: 0.08q2 + -0.08q2 = 0.00 -50 + 0.16q + -0.08q2 = 0.00 Begin completing the square. Divide all terms by -0.08 the coefficient of the squared term: Divide each side by '-0.08'. 625 + -2q + q2 = 0 Move the constant term to the right: Add '-625' to each side of the equation. 625 + -2q + -625 + q2 = 0 + -625 Reorder the terms: 625 + -625 + -2q + q2 = 0 + -625 Combine like terms: 625 + -625 = 0 0 + -2q + q2 = 0 + -625 -2q + q2 = 0 + -625 Combine like terms: 0 + -625 = -625 -2q + q2 = -625 The q term is -2q. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2q + 1 + q2 = -625 + 1 Reorder the terms: 1 + -2q + q2 = -625 + 1 Combine like terms: -625 + 1 = -624 1 + -2q + q2 = -624 Factor a perfect square on the left side: (q + -1)(q + -1) = -624 Can't calculate square root of the right side. The solution to this equation could not be determined.
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