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Simplifying 100 = -16t2 + 10t + 60 Reorder the terms: 100 = 60 + 10t + -16t2 Solving 100 = 60 + 10t + -16t2 Solving for variable 't'. Combine like terms: 100 + -60 = 40 40 + -10t + 16t2 = 60 + 10t + -16t2 + -60 + -10t + 16t2 Reorder the terms: 40 + -10t + 16t2 = 60 + -60 + 10t + -10t + -16t2 + 16t2 Combine like terms: 60 + -60 = 0 40 + -10t + 16t2 = 0 + 10t + -10t + -16t2 + 16t2 40 + -10t + 16t2 = 10t + -10t + -16t2 + 16t2 Combine like terms: 10t + -10t = 0 40 + -10t + 16t2 = 0 + -16t2 + 16t2 40 + -10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 40 + -10t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -5t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + -5t + 8t2)' equal to zero and attempt to solve: Simplifying 20 + -5t + 8t2 = 0 Solving 20 + -5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.5 + -0.625t + t2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -0.625t + -2.5 + t2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -0.625t + t2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -0.625t + t2 = 0 + -2.5 -0.625t + t2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -0.625t + t2 = -2.5 The t term is -0.625t. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625t + 0.09765625 + t2 = -2.5 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = -2.5 + 0.09765625 Combine like terms: -2.5 + 0.09765625 = -2.40234375 0.09765625 + -0.625t + t2 = -2.40234375 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = -2.40234375 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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