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Simplifying 0 = 16t2 + -24t + 20 Reorder the terms: 0 = 20 + -24t + 16t2 Solving 0 = 20 + -24t + 16t2 Solving for variable 't'. Combine like terms: 0 + -20 = -20 -20 + 24t + -16t2 = 20 + -24t + 16t2 + -20 + 24t + -16t2 Reorder the terms: -20 + 24t + -16t2 = 20 + -20 + -24t + 24t + 16t2 + -16t2 Combine like terms: 20 + -20 = 0 -20 + 24t + -16t2 = 0 + -24t + 24t + 16t2 + -16t2 -20 + 24t + -16t2 = -24t + 24t + 16t2 + -16t2 Combine like terms: -24t + 24t = 0 -20 + 24t + -16t2 = 0 + 16t2 + -16t2 -20 + 24t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -20 + 24t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 6t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 6t + -4t2)' equal to zero and attempt to solve: Simplifying -5 + 6t + -4t2 = 0 Solving -5 + 6t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.25 + -1.5t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -1.5t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -1.5t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -1.5t + t2 = 0 + -1.25 -1.5t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -1.5t + t2 = -1.25 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 = -1.25 + 0.5625 Reorder the terms: 0.5625 + -1.5t + t2 = -1.25 + 0.5625 Combine like terms: -1.25 + 0.5625 = -0.6875 0.5625 + -1.5t + t2 = -0.6875 Factor a perfect square on the left side: (t + -0.75)(t + -0.75) = -0.6875 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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