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Simplifying -16t2 + 48t + -40 = 0 Reorder the terms: -40 + 48t + -16t2 = 0 Solving -40 + 48t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(-5 + 6t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + 6t + -2t2)' equal to zero and attempt to solve: Simplifying -5 + 6t + -2t2 = 0 Solving -5 + 6t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -3t + t2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -3t + -2.5 + t2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -3t + t2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -3t + t2 = 0 + -2.5 -3t + t2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -3t + t2 = -2.5 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = -2.5 + 2.25 Reorder the terms: 2.25 + -3t + t2 = -2.5 + 2.25 Combine like terms: -2.5 + 2.25 = -0.25 2.25 + -3t + t2 = -0.25 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = -0.25 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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