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Simplifying -3Q2 + -27Q = 1400 Reorder the terms: -27Q + -3Q2 = 1400 Solving -27Q + -3Q2 = 1400 Solving for variable 'Q'. Reorder the terms: -1400 + -27Q + -3Q2 = 1400 + -1400 Combine like terms: 1400 + -1400 = 0 -1400 + -27Q + -3Q2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1400 + 27Q + 3Q2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1400 + 27Q + 3Q2)' equal to zero and attempt to solve: Simplifying 1400 + 27Q + 3Q2 = 0 Solving 1400 + 27Q + 3Q2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 466.6666667 + 9Q + Q2 = 0 Move the constant term to the right: Add '-466.6666667' to each side of the equation. 466.6666667 + 9Q + -466.6666667 + Q2 = 0 + -466.6666667 Reorder the terms: 466.6666667 + -466.6666667 + 9Q + Q2 = 0 + -466.6666667 Combine like terms: 466.6666667 + -466.6666667 = 0.0000000 0.0000000 + 9Q + Q2 = 0 + -466.6666667 9Q + Q2 = 0 + -466.6666667 Combine like terms: 0 + -466.6666667 = -466.6666667 9Q + Q2 = -466.6666667 The Q term is 9Q. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9Q + 20.25 + Q2 = -466.6666667 + 20.25 Reorder the terms: 20.25 + 9Q + Q2 = -466.6666667 + 20.25 Combine like terms: -466.6666667 + 20.25 = -446.4166667 20.25 + 9Q + Q2 = -446.4166667 Factor a perfect square on the left side: (Q + 4.5)(Q + 4.5) = -446.4166667 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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