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Simplifying 400 = -16t2 + 150t Reorder the terms: 400 = 150t + -16t2 Solving 400 = 150t + -16t2 Solving for variable 't'. Reorder the terms: 400 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 400 + -150t + 16t2 = 0 + -16t2 + 16t2 400 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 400 + -150t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(200 + -75t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(200 + -75t + 8t2)' equal to zero and attempt to solve: Simplifying 200 + -75t + 8t2 = 0 Solving 200 + -75t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 25 + -9.375t + t2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -9.375t + -25 + t2 = 0 + -25 Reorder the terms: 25 + -25 + -9.375t + t2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -9.375t + t2 = 0 + -25 -9.375t + t2 = 0 + -25 Combine like terms: 0 + -25 = -25 -9.375t + t2 = -25 The t term is -9.375t. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375t + 21.97265625 + t2 = -25 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = -25 + 21.97265625 Combine like terms: -25 + 21.97265625 = -3.02734375 21.97265625 + -9.375t + t2 = -3.02734375 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = -3.02734375 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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