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Simplifying 12 = -16t2 + 20t + 5 Reorder the terms: 12 = 5 + 20t + -16t2 Solving 12 = 5 + 20t + -16t2 Solving for variable 't'. Combine like terms: 12 + -5 = 7 7 + -20t + 16t2 = 5 + 20t + -16t2 + -5 + -20t + 16t2 Reorder the terms: 7 + -20t + 16t2 = 5 + -5 + 20t + -20t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 7 + -20t + 16t2 = 0 + 20t + -20t + -16t2 + 16t2 7 + -20t + 16t2 = 20t + -20t + -16t2 + 16t2 Combine like terms: 20t + -20t = 0 7 + -20t + 16t2 = 0 + -16t2 + 16t2 7 + -20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 7 + -20t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.4375 + -1.25t + t2 = 0 Move the constant term to the right: Add '-0.4375' to each side of the equation. 0.4375 + -1.25t + -0.4375 + t2 = 0 + -0.4375 Reorder the terms: 0.4375 + -0.4375 + -1.25t + t2 = 0 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + -1.25t + t2 = 0 + -0.4375 -1.25t + t2 = 0 + -0.4375 Combine like terms: 0 + -0.4375 = -0.4375 -1.25t + t2 = -0.4375 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 = -0.4375 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = -0.4375 + 0.390625 Combine like terms: -0.4375 + 0.390625 = -0.046875 0.390625 + -1.25t + t2 = -0.046875 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = -0.046875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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