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Simplifying 98 + 2q + 2q2 = 2 + 4q Solving 98 + 2q + 2q2 = 2 + 4q Solving for variable 'q'. Reorder the terms: 98 + -2 + 2q + -4q + 2q2 = 2 + 4q + -2 + -4q Combine like terms: 98 + -2 = 96 96 + 2q + -4q + 2q2 = 2 + 4q + -2 + -4q Combine like terms: 2q + -4q = -2q 96 + -2q + 2q2 = 2 + 4q + -2 + -4q Reorder the terms: 96 + -2q + 2q2 = 2 + -2 + 4q + -4q Combine like terms: 2 + -2 = 0 96 + -2q + 2q2 = 0 + 4q + -4q 96 + -2q + 2q2 = 4q + -4q Combine like terms: 4q + -4q = 0 96 + -2q + 2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(48 + -1q + q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(48 + -1q + q2)' equal to zero and attempt to solve: Simplifying 48 + -1q + q2 = 0 Solving 48 + -1q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -1q + -48 + q2 = 0 + -48 Reorder the terms: 48 + -48 + -1q + q2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -1q + q2 = 0 + -48 -1q + q2 = 0 + -48 Combine like terms: 0 + -48 = -48 -1q + q2 = -48 The q term is -1q. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1q + 0.25 + q2 = -48 + 0.25 Reorder the terms: 0.25 + -1q + q2 = -48 + 0.25 Combine like terms: -48 + 0.25 = -47.75 0.25 + -1q + q2 = -47.75 Factor a perfect square on the left side: (q + -0.5)(q + -0.5) = -47.75 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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