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Simplifying 35 = 10q + -25q2 Solving 35 = 10q + -25q2 Solving for variable 'q'. Reorder the terms: 35 + -10q + 25q2 = 10q + -10q + -25q2 + 25q2 Combine like terms: 10q + -10q = 0 35 + -10q + 25q2 = 0 + -25q2 + 25q2 35 + -10q + 25q2 = -25q2 + 25q2 Combine like terms: -25q2 + 25q2 = 0 35 + -10q + 25q2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(7 + -2q + 5q2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + -2q + 5q2)' equal to zero and attempt to solve: Simplifying 7 + -2q + 5q2 = 0 Solving 7 + -2q + 5q2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -0.4q + q2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -0.4q + -1.4 + q2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -0.4q + q2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -0.4q + q2 = 0 + -1.4 -0.4q + q2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -0.4q + q2 = -1.4 The q term is -0.4q. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4q + 0.04 + q2 = -1.4 + 0.04 Reorder the terms: 0.04 + -0.4q + q2 = -1.4 + 0.04 Combine like terms: -1.4 + 0.04 = -1.36 0.04 + -0.4q + q2 = -1.36 Factor a perfect square on the left side: (q + -0.2)(q + -0.2) = -1.36 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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