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Simplifying 150 = -16t2 + 118t + 3 Reorder the terms: 150 = 3 + 118t + -16t2 Solving 150 = 3 + 118t + -16t2 Solving for variable 't'. Combine like terms: 150 + -3 = 147 147 + -118t + 16t2 = 3 + 118t + -16t2 + -3 + -118t + 16t2 Reorder the terms: 147 + -118t + 16t2 = 3 + -3 + 118t + -118t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 147 + -118t + 16t2 = 0 + 118t + -118t + -16t2 + 16t2 147 + -118t + 16t2 = 118t + -118t + -16t2 + 16t2 Combine like terms: 118t + -118t = 0 147 + -118t + 16t2 = 0 + -16t2 + 16t2 147 + -118t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 147 + -118t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 9.1875 + -7.375t + t2 = 0 Move the constant term to the right: Add '-9.1875' to each side of the equation. 9.1875 + -7.375t + -9.1875 + t2 = 0 + -9.1875 Reorder the terms: 9.1875 + -9.1875 + -7.375t + t2 = 0 + -9.1875 Combine like terms: 9.1875 + -9.1875 = 0.0000 0.0000 + -7.375t + t2 = 0 + -9.1875 -7.375t + t2 = 0 + -9.1875 Combine like terms: 0 + -9.1875 = -9.1875 -7.375t + t2 = -9.1875 The t term is -7.375t. Take half its coefficient (-3.6875). Square it (13.59765625) and add it to both sides. Add '13.59765625' to each side of the equation. -7.375t + 13.59765625 + t2 = -9.1875 + 13.59765625 Reorder the terms: 13.59765625 + -7.375t + t2 = -9.1875 + 13.59765625 Combine like terms: -9.1875 + 13.59765625 = 4.41015625 13.59765625 + -7.375t + t2 = 4.41015625 Factor a perfect square on the left side: (t + -3.6875)(t + -3.6875) = 4.41015625 Calculate the square root of the right side: 2.100037202 Break this problem into two subproblems by setting (t + -3.6875) equal to 2.100037202 and -2.100037202.Subproblem 1
t + -3.6875 = 2.100037202 Simplifying t + -3.6875 = 2.100037202 Reorder the terms: -3.6875 + t = 2.100037202 Solving -3.6875 + t = 2.100037202 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + t = 2.100037202 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + t = 2.100037202 + 3.6875 t = 2.100037202 + 3.6875 Combine like terms: 2.100037202 + 3.6875 = 5.787537202 t = 5.787537202 Simplifying t = 5.787537202Subproblem 2
t + -3.6875 = -2.100037202 Simplifying t + -3.6875 = -2.100037202 Reorder the terms: -3.6875 + t = -2.100037202 Solving -3.6875 + t = -2.100037202 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + t = -2.100037202 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + t = -2.100037202 + 3.6875 t = -2.100037202 + 3.6875 Combine like terms: -2.100037202 + 3.6875 = 1.587462798 t = 1.587462798 Simplifying t = 1.587462798Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.787537202, 1.587462798}
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