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Simplifying -272 = 16t2 + -32t Reorder the terms: -272 = -32t + 16t2 Solving -272 = -32t + 16t2 Solving for variable 't'. Reorder the terms: -272 + 32t + -16t2 = -32t + 32t + 16t2 + -16t2 Combine like terms: -32t + 32t = 0 -272 + 32t + -16t2 = 0 + 16t2 + -16t2 -272 + 32t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -272 + 32t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-17 + 2t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-17 + 2t + -1t2)' equal to zero and attempt to solve: Simplifying -17 + 2t + -1t2 = 0 Solving -17 + 2t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 17 + -2t + t2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + -2t + -17 + t2 = 0 + -17 Reorder the terms: 17 + -17 + -2t + t2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -2t + t2 = 0 + -17 -2t + t2 = 0 + -17 Combine like terms: 0 + -17 = -17 -2t + t2 = -17 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = -17 + 1 Reorder the terms: 1 + -2t + t2 = -17 + 1 Combine like terms: -17 + 1 = -16 1 + -2t + t2 = -16 Factor a perfect square on the left side: (t + -1)(t + -1) = -16 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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