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Simplifying 20 = -16t2 + 20t + 2 Reorder the terms: 20 = 2 + 20t + -16t2 Solving 20 = 2 + 20t + -16t2 Solving for variable 't'. Combine like terms: 20 + -2 = 18 18 + -20t + 16t2 = 2 + 20t + -16t2 + -2 + -20t + 16t2 Reorder the terms: 18 + -20t + 16t2 = 2 + -2 + 20t + -20t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 18 + -20t + 16t2 = 0 + 20t + -20t + -16t2 + 16t2 18 + -20t + 16t2 = 20t + -20t + -16t2 + 16t2 Combine like terms: 20t + -20t = 0 18 + -20t + 16t2 = 0 + -16t2 + 16t2 18 + -20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 18 + -20t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -10t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -10t + 8t2)' equal to zero and attempt to solve: Simplifying 9 + -10t + 8t2 = 0 Solving 9 + -10t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + -1.25t + t2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -1.25t + -1.125 + t2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -1.25t + t2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -1.25t + t2 = 0 + -1.125 -1.25t + t2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -1.25t + t2 = -1.125 The t term is -1.25t. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25t + 0.390625 + t2 = -1.125 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = -1.125 + 0.390625 Combine like terms: -1.125 + 0.390625 = -0.734375 0.390625 + -1.25t + t2 = -0.734375 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = -0.734375 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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