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Simplifying 100 = 20q + -2q2 Solving 100 = 20q + -2q2 Solving for variable 'q'. Reorder the terms: 100 + -20q + 2q2 = 20q + -20q + -2q2 + 2q2 Combine like terms: 20q + -20q = 0 100 + -20q + 2q2 = 0 + -2q2 + 2q2 100 + -20q + 2q2 = -2q2 + 2q2 Combine like terms: -2q2 + 2q2 = 0 100 + -20q + 2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(50 + -10q + q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + -10q + q2)' equal to zero and attempt to solve: Simplifying 50 + -10q + q2 = 0 Solving 50 + -10q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -10q + -50 + q2 = 0 + -50 Reorder the terms: 50 + -50 + -10q + q2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -10q + q2 = 0 + -50 -10q + q2 = 0 + -50 Combine like terms: 0 + -50 = -50 -10q + q2 = -50 The q term is -10q. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10q + 25 + q2 = -50 + 25 Reorder the terms: 25 + -10q + q2 = -50 + 25 Combine like terms: -50 + 25 = -25 25 + -10q + q2 = -25 Factor a perfect square on the left side: (q + -5)(q + -5) = -25 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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