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Simplifying -16t2 + 40t + -48 = 0 Reorder the terms: -48 + 40t + -16t2 = 0 Solving -48 + 40t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(-6 + 5t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-6 + 5t + -2t2)' equal to zero and attempt to solve: Simplifying -6 + 5t + -2t2 = 0 Solving -6 + 5t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 3 + -2.5t + t2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2.5t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + -2.5t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2.5t + t2 = 0 + -3 -2.5t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2.5t + t2 = -3 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = -3 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = -3 + 1.5625 Combine like terms: -3 + 1.5625 = -1.4375 1.5625 + -2.5t + t2 = -1.4375 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = -1.4375 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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