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Simplifying 4q2 + 100 = 8q Reorder the terms: 100 + 4q2 = 8q Solving 100 + 4q2 = 8q Solving for variable 'q'. Reorder the terms: 100 + -8q + 4q2 = 8q + -8q Combine like terms: 8q + -8q = 0 100 + -8q + 4q2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(25 + -2q + q2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + -2q + q2)' equal to zero and attempt to solve: Simplifying 25 + -2q + q2 = 0 Solving 25 + -2q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -2q + -25 + q2 = 0 + -25 Reorder the terms: 25 + -25 + -2q + q2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -2q + q2 = 0 + -25 -2q + q2 = 0 + -25 Combine like terms: 0 + -25 = -25 -2q + q2 = -25 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 = -25 + 1 Reorder the terms: 1 + -2q + q2 = -25 + 1 Combine like terms: -25 + 1 = -24 1 + -2q + q2 = -24 Factor a perfect square on the left side: (q + -1)(q + -1) = -24 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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