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Simplifying 2400 + 6Q2 = 12Q Solving 2400 + 6Q2 = 12Q Solving for variable 'Q'. Reorder the terms: 2400 + -12Q + 6Q2 = 12Q + -12Q Combine like terms: 12Q + -12Q = 0 2400 + -12Q + 6Q2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(400 + -2Q + Q2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(400 + -2Q + Q2)' equal to zero and attempt to solve: Simplifying 400 + -2Q + Q2 = 0 Solving 400 + -2Q + Q2 = 0 Begin completing the square. Move the constant term to the right: Add '-400' to each side of the equation. 400 + -2Q + -400 + Q2 = 0 + -400 Reorder the terms: 400 + -400 + -2Q + Q2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -2Q + Q2 = 0 + -400 -2Q + Q2 = 0 + -400 Combine like terms: 0 + -400 = -400 -2Q + Q2 = -400 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 = -400 + 1 Reorder the terms: 1 + -2Q + Q2 = -400 + 1 Combine like terms: -400 + 1 = -399 1 + -2Q + Q2 = -399 Factor a perfect square on the left side: (Q + -1)(Q + -1) = -399 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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