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Simplifying 32 = -16t(t) + 8t + 24 Multiply t * t 32 = -16t2 + 8t + 24 Reorder the terms: 32 = 24 + 8t + -16t2 Solving 32 = 24 + 8t + -16t2 Solving for variable 't'. Combine like terms: 32 + -24 = 8 8 + -8t + 16t2 = 24 + 8t + -16t2 + -24 + -8t + 16t2 Reorder the terms: 8 + -8t + 16t2 = 24 + -24 + 8t + -8t + -16t2 + 16t2 Combine like terms: 24 + -24 = 0 8 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2 8 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2 Combine like terms: 8t + -8t = 0 8 + -8t + 16t2 = 0 + -16t2 + 16t2 8 + -8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 8 + -8t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(1 + -1t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + -1t + 2t2)' equal to zero and attempt to solve: Simplifying 1 + -1t + 2t2 = 0 Solving 1 + -1t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -0.5t + t2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.5t + -0.5 + t2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.5t + t2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.5t + t2 = 0 + -0.5 -0.5t + t2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.5t + t2 = -0.5 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = -0.5 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = -0.5 + 0.0625 Combine like terms: -0.5 + 0.0625 = -0.4375 0.0625 + -0.5t + t2 = -0.4375 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = -0.4375 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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