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Simplifying -16t2 + 176t + -480 = 480 Reorder the terms: -480 + 176t + -16t2 = 480 Solving -480 + 176t + -16t2 = 480 Solving for variable 't'. Reorder the terms: -480 + -480 + 176t + -16t2 = 480 + -480 Combine like terms: -480 + -480 = -960 -960 + 176t + -16t2 = 480 + -480 Combine like terms: 480 + -480 = 0 -960 + 176t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-60 + 11t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-60 + 11t + -1t2)' equal to zero and attempt to solve: Simplifying -60 + 11t + -1t2 = 0 Solving -60 + 11t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 60 + -11t + t2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -11t + -60 + t2 = 0 + -60 Reorder the terms: 60 + -60 + -11t + t2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -11t + t2 = 0 + -60 -11t + t2 = 0 + -60 Combine like terms: 0 + -60 = -60 -11t + t2 = -60 The t term is -11t. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11t + 30.25 + t2 = -60 + 30.25 Reorder the terms: 30.25 + -11t + t2 = -60 + 30.25 Combine like terms: -60 + 30.25 = -29.75 30.25 + -11t + t2 = -29.75 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = -29.75 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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