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Simplifying -16t2 + 32t + -48 = 0 Reorder the terms: -48 + 32t + -16t2 = 0 Solving -48 + 32t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(-3 + 2t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-3 + 2t + -1t2)' equal to zero and attempt to solve: Simplifying -3 + 2t + -1t2 = 0 Solving -3 + 2t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -2t + t2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + -2t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t + t2 = 0 + -3 -2t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2t + t2 = -3 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 = -3 + 1 Reorder the terms: 1 + -2t + t2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + -2t + t2 = -2 Factor a perfect square on the left side: (t + -1)(t + -1) = -2 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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