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Simplifying 0 = 100t + -16t2 + -2000 Reorder the terms: 0 = -2000 + 100t + -16t2 Solving 0 = -2000 + 100t + -16t2 Solving for variable 't'. Combine like terms: 0 + 2000 = 2000 2000 + -100t + 16t2 = -2000 + 100t + -16t2 + 2000 + -100t + 16t2 Reorder the terms: 2000 + -100t + 16t2 = -2000 + 2000 + 100t + -100t + -16t2 + 16t2 Combine like terms: -2000 + 2000 = 0 2000 + -100t + 16t2 = 0 + 100t + -100t + -16t2 + 16t2 2000 + -100t + 16t2 = 100t + -100t + -16t2 + 16t2 Combine like terms: 100t + -100t = 0 2000 + -100t + 16t2 = 0 + -16t2 + 16t2 2000 + -100t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 2000 + -100t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(500 + -25t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(500 + -25t + 4t2)' equal to zero and attempt to solve: Simplifying 500 + -25t + 4t2 = 0 Solving 500 + -25t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 125 + -6.25t + t2 = 0 Move the constant term to the right: Add '-125' to each side of the equation. 125 + -6.25t + -125 + t2 = 0 + -125 Reorder the terms: 125 + -125 + -6.25t + t2 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -6.25t + t2 = 0 + -125 -6.25t + t2 = 0 + -125 Combine like terms: 0 + -125 = -125 -6.25t + t2 = -125 The t term is -6.25t. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25t + 9.765625 + t2 = -125 + 9.765625 Reorder the terms: 9.765625 + -6.25t + t2 = -125 + 9.765625 Combine like terms: -125 + 9.765625 = -115.234375 9.765625 + -6.25t + t2 = -115.234375 Factor a perfect square on the left side: (t + -3.125)(t + -3.125) = -115.234375 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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