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Simplifying -16t2 + 16t + -480 = 0 Reorder the terms: -480 + 16t + -16t2 = 0 Solving -480 + 16t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(-30 + t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-30 + t + -1t2)' equal to zero and attempt to solve: Simplifying -30 + t + -1t2 = 0 Solving -30 + t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 30 + -1t + t2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -1t + -30 + t2 = 0 + -30 Reorder the terms: 30 + -30 + -1t + t2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1t + t2 = 0 + -30 -1t + t2 = 0 + -30 Combine like terms: 0 + -30 = -30 -1t + t2 = -30 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = -30 + 0.25 Reorder the terms: 0.25 + -1t + t2 = -30 + 0.25 Combine like terms: -30 + 0.25 = -29.75 0.25 + -1t + t2 = -29.75 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -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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