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Simplifying 0 = 16t2 + 50t + 200 Reorder the terms: 0 = 200 + 50t + 16t2 Solving 0 = 200 + 50t + 16t2 Solving for variable 't'. Combine like terms: 0 + -200 = -200 -200 + -50t + -16t2 = 200 + 50t + 16t2 + -200 + -50t + -16t2 Reorder the terms: -200 + -50t + -16t2 = 200 + -200 + 50t + -50t + 16t2 + -16t2 Combine like terms: 200 + -200 = 0 -200 + -50t + -16t2 = 0 + 50t + -50t + 16t2 + -16t2 -200 + -50t + -16t2 = 50t + -50t + 16t2 + -16t2 Combine like terms: 50t + -50t = 0 -200 + -50t + -16t2 = 0 + 16t2 + -16t2 -200 + -50t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -200 + -50t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(100 + 25t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(100 + 25t + 8t2)' equal to zero and attempt to solve: Simplifying 100 + 25t + 8t2 = 0 Solving 100 + 25t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 12.5 + 3.125t + t2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 3.125t + -12.5 + t2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 3.125t + t2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 3.125t + t2 = 0 + -12.5 3.125t + t2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 3.125t + t2 = -12.5 The t term is 3.125t. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125t + 2.44140625 + t2 = -12.5 + 2.44140625 Reorder the terms: 2.44140625 + 3.125t + t2 = -12.5 + 2.44140625 Combine like terms: -12.5 + 2.44140625 = -10.05859375 2.44140625 + 3.125t + t2 = -10.05859375 Factor a perfect square on the left side: (t + 1.5625)(t + 1.5625) = -10.05859375 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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