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Simplifying 2q = q2 + 100 Reorder the terms: 2q = 100 + q2 Solving 2q = 100 + q2 Solving for variable 'q'. Reorder the terms: -100 + 2q + -1q2 = 100 + q2 + -100 + -1q2 Reorder the terms: -100 + 2q + -1q2 = 100 + -100 + q2 + -1q2 Combine like terms: 100 + -100 = 0 -100 + 2q + -1q2 = 0 + q2 + -1q2 -100 + 2q + -1q2 = q2 + -1q2 Combine like terms: q2 + -1q2 = 0 -100 + 2q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 100 + -2q + q2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -2q + -100 + q2 = 0 + -100 Reorder the terms: 100 + -100 + -2q + q2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -2q + q2 = 0 + -100 -2q + q2 = 0 + -100 Combine like terms: 0 + -100 = -100 -2q + q2 = -100 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 = -100 + 1 Reorder the terms: 1 + -2q + q2 = -100 + 1 Combine like terms: -100 + 1 = -99 1 + -2q + q2 = -99 Factor a perfect square on the left side: (q + -1)(q + -1) = -99 Can't calculate square root of the right side. The solution to this equation could not be determined.
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