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Simplifying 24 = 24t + -16t2 Solving 24 = 24t + -16t2 Solving for variable 't'. Reorder the terms: 24 + -24t + 16t2 = 24t + -24t + -16t2 + 16t2 Combine like terms: 24t + -24t = 0 24 + -24t + 16t2 = 0 + -16t2 + 16t2 24 + -24t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 24 + -24t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(3 + -3t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(3 + -3t + 2t2)' equal to zero and attempt to solve: Simplifying 3 + -3t + 2t2 = 0 Solving 3 + -3t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -1.5t + t2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -1.5t + -1.5 + t2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -1.5t + t2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -1.5t + t2 = 0 + -1.5 -1.5t + t2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -1.5t + t2 = -1.5 The t term is -1.5t. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5t + 0.5625 + t2 = -1.5 + 0.5625 Reorder the terms: 0.5625 + -1.5t + t2 = -1.5 + 0.5625 Combine like terms: -1.5 + 0.5625 = -0.9375 0.5625 + -1.5t + t2 = -0.9375 Factor a perfect square on the left side: (t + -0.75)(t + -0.75) = -0.9375 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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