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Simplifying 48t2 + -28t + 6 = 0 Reorder the terms: 6 + -28t + 48t2 = 0 Solving 6 + -28t + 48t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -14t + 24t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -14t + 24t2)' equal to zero and attempt to solve: Simplifying 3 + -14t + 24t2 = 0 Solving 3 + -14t + 24t2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.125 + -0.5833333333t + t2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -0.5833333333t + -0.125 + t2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -0.5833333333t + t2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -0.5833333333t + t2 = 0 + -0.125 -0.5833333333t + t2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -0.5833333333t + t2 = -0.125 The t term is -0.5833333333t. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333t + 0.08506944446 + t2 = -0.125 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333t + t2 = -0.125 + 0.08506944446 Combine like terms: -0.125 + 0.08506944446 = -0.03993055554 0.08506944446 + -0.5833333333t + t2 = -0.03993055554 Factor a perfect square on the left side: (t + -0.2916666667)(t + -0.2916666667) = -0.03993055554 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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