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Simplifying -16t2 + 90t + 0 = 480 Reorder the terms: 0 + 90t + -16t2 = 480 Remove the zero: 90t + -16t2 = 480 Solving 90t + -16t2 = 480 Solving for variable 't'. Reorder the terms: -480 + 90t + -16t2 = 480 + -480 Combine like terms: 480 + -480 = 0 -480 + 90t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-240 + 45t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-240 + 45t + -8t2)' equal to zero and attempt to solve: Simplifying -240 + 45t + -8t2 = 0 Solving -240 + 45t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 30 + -5.625t + t2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -5.625t + -30 + t2 = 0 + -30 Reorder the terms: 30 + -30 + -5.625t + t2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -5.625t + t2 = 0 + -30 -5.625t + t2 = 0 + -30 Combine like terms: 0 + -30 = -30 -5.625t + t2 = -30 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 = -30 + 7.91015625 Reorder the terms: 7.91015625 + -5.625t + t2 = -30 + 7.91015625 Combine like terms: -30 + 7.91015625 = -22.08984375 7.91015625 + -5.625t + t2 = -22.08984375 Factor a perfect square on the left side: (t + -2.8125)(t + -2.8125) = -22.08984375 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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