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Simplifying 0 = 16 + 3Q2 + 2Q Reorder the terms: 0 = 16 + 2Q + 3Q2 Solving 0 = 16 + 2Q + 3Q2 Solving for variable 'Q'. Combine like terms: 0 + -16 = -16 -16 + -2Q + -3Q2 = 16 + 2Q + 3Q2 + -16 + -2Q + -3Q2 Reorder the terms: -16 + -2Q + -3Q2 = 16 + -16 + 2Q + -2Q + 3Q2 + -3Q2 Combine like terms: 16 + -16 = 0 -16 + -2Q + -3Q2 = 0 + 2Q + -2Q + 3Q2 + -3Q2 -16 + -2Q + -3Q2 = 2Q + -2Q + 3Q2 + -3Q2 Combine like terms: 2Q + -2Q = 0 -16 + -2Q + -3Q2 = 0 + 3Q2 + -3Q2 -16 + -2Q + -3Q2 = 3Q2 + -3Q2 Combine like terms: 3Q2 + -3Q2 = 0 -16 + -2Q + -3Q2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 2Q + 3Q2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 2Q + 3Q2)' equal to zero and attempt to solve: Simplifying 16 + 2Q + 3Q2 = 0 Solving 16 + 2Q + 3Q2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.333333333 + 0.6666666667Q + Q2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + 0.6666666667Q + -5.333333333 + Q2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + 0.6666666667Q + Q2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + 0.6666666667Q + Q2 = 0 + -5.333333333 0.6666666667Q + Q2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 0.6666666667Q + Q2 = -5.333333333 The Q term is 0.6666666667Q. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667Q + 0.1111111112 + Q2 = -5.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667Q + Q2 = -5.333333333 + 0.1111111112 Combine like terms: -5.333333333 + 0.1111111112 = -5.2222222218 0.1111111112 + 0.6666666667Q + Q2 = -5.2222222218 Factor a perfect square on the left side: (Q + 0.3333333334)(Q + 0.3333333334) = -5.2222222218 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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