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Simplifying 0 = 16t2 + 9t + 46 Reorder the terms: 0 = 46 + 9t + 16t2 Solving 0 = 46 + 9t + 16t2 Solving for variable 't'. Combine like terms: 0 + -46 = -46 -46 + -9t + -16t2 = 46 + 9t + 16t2 + -46 + -9t + -16t2 Reorder the terms: -46 + -9t + -16t2 = 46 + -46 + 9t + -9t + 16t2 + -16t2 Combine like terms: 46 + -46 = 0 -46 + -9t + -16t2 = 0 + 9t + -9t + 16t2 + -16t2 -46 + -9t + -16t2 = 9t + -9t + 16t2 + -16t2 Combine like terms: 9t + -9t = 0 -46 + -9t + -16t2 = 0 + 16t2 + -16t2 -46 + -9t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -46 + -9t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(46 + 9t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(46 + 9t + 16t2)' equal to zero and attempt to solve: Simplifying 46 + 9t + 16t2 = 0 Solving 46 + 9t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.875 + 0.5625t + t2 = 0 Move the constant term to the right: Add '-2.875' to each side of the equation. 2.875 + 0.5625t + -2.875 + t2 = 0 + -2.875 Reorder the terms: 2.875 + -2.875 + 0.5625t + t2 = 0 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + 0.5625t + t2 = 0 + -2.875 0.5625t + t2 = 0 + -2.875 Combine like terms: 0 + -2.875 = -2.875 0.5625t + t2 = -2.875 The t term is 0.5625t. Take half its coefficient (0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. 0.5625t + 0.0791015625 + t2 = -2.875 + 0.0791015625 Reorder the terms: 0.0791015625 + 0.5625t + t2 = -2.875 + 0.0791015625 Combine like terms: -2.875 + 0.0791015625 = -2.7958984375 0.0791015625 + 0.5625t + t2 = -2.7958984375 Factor a perfect square on the left side: (t + 0.28125)(t + 0.28125) = -2.7958984375 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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