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Simplifying 0 = 16t2 + 90t + 252 Reorder the terms: 0 = 252 + 90t + 16t2 Solving 0 = 252 + 90t + 16t2 Solving for variable 't'. Combine like terms: 0 + -252 = -252 -252 + -90t + -16t2 = 252 + 90t + 16t2 + -252 + -90t + -16t2 Reorder the terms: -252 + -90t + -16t2 = 252 + -252 + 90t + -90t + 16t2 + -16t2 Combine like terms: 252 + -252 = 0 -252 + -90t + -16t2 = 0 + 90t + -90t + 16t2 + -16t2 -252 + -90t + -16t2 = 90t + -90t + 16t2 + -16t2 Combine like terms: 90t + -90t = 0 -252 + -90t + -16t2 = 0 + 16t2 + -16t2 -252 + -90t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -252 + -90t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(126 + 45t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(126 + 45t + 8t2)' equal to zero and attempt to solve: Simplifying 126 + 45t + 8t2 = 0 Solving 126 + 45t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 15.75 + 5.625t + t2 = 0 Move the constant term to the right: Add '-15.75' to each side of the equation. 15.75 + 5.625t + -15.75 + t2 = 0 + -15.75 Reorder the terms: 15.75 + -15.75 + 5.625t + t2 = 0 + -15.75 Combine like terms: 15.75 + -15.75 = 0.00 0.00 + 5.625t + t2 = 0 + -15.75 5.625t + t2 = 0 + -15.75 Combine like terms: 0 + -15.75 = -15.75 5.625t + t2 = -15.75 The t term is 5.625t. Take half its coefficient (2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. 5.625t + 7.91015625 + t2 = -15.75 + 7.91015625 Reorder the terms: 7.91015625 + 5.625t + t2 = -15.75 + 7.91015625 Combine like terms: -15.75 + 7.91015625 = -7.83984375 7.91015625 + 5.625t + t2 = -7.83984375 Factor a perfect square on the left side: (t + 2.8125)(t + 2.8125) = -7.83984375 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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