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Simplifying 75q = q2 + 6250 Reorder the terms: 75q = 6250 + q2 Solving 75q = 6250 + q2 Solving for variable 'q'. Reorder the terms: -6250 + 75q + -1q2 = 6250 + q2 + -6250 + -1q2 Reorder the terms: -6250 + 75q + -1q2 = 6250 + -6250 + q2 + -1q2 Combine like terms: 6250 + -6250 = 0 -6250 + 75q + -1q2 = 0 + q2 + -1q2 -6250 + 75q + -1q2 = q2 + -1q2 Combine like terms: q2 + -1q2 = 0 -6250 + 75q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6250 + -75q + q2 = 0 Move the constant term to the right: Add '-6250' to each side of the equation. 6250 + -75q + -6250 + q2 = 0 + -6250 Reorder the terms: 6250 + -6250 + -75q + q2 = 0 + -6250 Combine like terms: 6250 + -6250 = 0 0 + -75q + q2 = 0 + -6250 -75q + q2 = 0 + -6250 Combine like terms: 0 + -6250 = -6250 -75q + q2 = -6250 The q term is -75q. Take half its coefficient (-37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. -75q + 1406.25 + q2 = -6250 + 1406.25 Reorder the terms: 1406.25 + -75q + q2 = -6250 + 1406.25 Combine like terms: -6250 + 1406.25 = -4843.75 1406.25 + -75q + q2 = -4843.75 Factor a perfect square on the left side: (q + -37.5)(q + -37.5) = -4843.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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