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Simplifying 12q2 = 34q + -28 Reorder the terms: 12q2 = -28 + 34q Solving 12q2 = -28 + 34q Solving for variable 'q'. Reorder the terms: 28 + -34q + 12q2 = -28 + 34q + 28 + -34q Reorder the terms: 28 + -34q + 12q2 = -28 + 28 + 34q + -34q Combine like terms: -28 + 28 = 0 28 + -34q + 12q2 = 0 + 34q + -34q 28 + -34q + 12q2 = 34q + -34q Combine like terms: 34q + -34q = 0 28 + -34q + 12q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -17q + 6q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + -17q + 6q2)' equal to zero and attempt to solve: Simplifying 14 + -17q + 6q2 = 0 Solving 14 + -17q + 6q2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.333333333 + -2.833333333q + q2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -2.833333333q + -2.333333333 + q2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -2.833333333q + q2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -2.833333333q + q2 = 0 + -2.333333333 -2.833333333q + q2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -2.833333333q + q2 = -2.333333333 The q term is -2.833333333q. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333q + 2.006944445 + q2 = -2.333333333 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333q + q2 = -2.333333333 + 2.006944445 Combine like terms: -2.333333333 + 2.006944445 = -0.326388888 2.006944445 + -2.833333333q + q2 = -0.326388888 Factor a perfect square on the left side: (q + -1.416666667)(q + -1.416666667) = -0.326388888 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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