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Simplifying -16t2 + 60t + 6 = 45 Reorder the terms: 6 + 60t + -16t2 = 45 Solving 6 + 60t + -16t2 = 45 Solving for variable 't'. Reorder the terms: 6 + -45 + 60t + -16t2 = 45 + -45 Combine like terms: 6 + -45 = -39 -39 + 60t + -16t2 = 45 + -45 Combine like terms: 45 + -45 = 0 -39 + 60t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 2.4375 + -3.75t + t2 = 0 Move the constant term to the right: Add '-2.4375' to each side of the equation. 2.4375 + -3.75t + -2.4375 + t2 = 0 + -2.4375 Reorder the terms: 2.4375 + -2.4375 + -3.75t + t2 = 0 + -2.4375 Combine like terms: 2.4375 + -2.4375 = 0.0000 0.0000 + -3.75t + t2 = 0 + -2.4375 -3.75t + t2 = 0 + -2.4375 Combine like terms: 0 + -2.4375 = -2.4375 -3.75t + t2 = -2.4375 The t term is -3.75t. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75t + 3.515625 + t2 = -2.4375 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = -2.4375 + 3.515625 Combine like terms: -2.4375 + 3.515625 = 1.078125 3.515625 + -3.75t + t2 = 1.078125 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 1.078125 Calculate the square root of the right side: 1.038327983 Break this problem into two subproblems by setting (t + -1.875) equal to 1.038327983 and -1.038327983.Subproblem 1
t + -1.875 = 1.038327983 Simplifying t + -1.875 = 1.038327983 Reorder the terms: -1.875 + t = 1.038327983 Solving -1.875 + t = 1.038327983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = 1.038327983 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 1.038327983 + 1.875 t = 1.038327983 + 1.875 Combine like terms: 1.038327983 + 1.875 = 2.913327983 t = 2.913327983 Simplifying t = 2.913327983Subproblem 2
t + -1.875 = -1.038327983 Simplifying t + -1.875 = -1.038327983 Reorder the terms: -1.875 + t = -1.038327983 Solving -1.875 + t = -1.038327983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = -1.038327983 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -1.038327983 + 1.875 t = -1.038327983 + 1.875 Combine like terms: -1.038327983 + 1.875 = 0.836672017 t = 0.836672017 Simplifying t = 0.836672017Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.913327983, 0.836672017}
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