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Simplifying -16t2 + 60t + 45 = 0 Reorder the terms: 45 + 60t + -16t2 = 0 Solving 45 + 60t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.8125 + -3.75t + t2 = 0 Move the constant term to the right: Add '2.8125' to each side of the equation. -2.8125 + -3.75t + 2.8125 + t2 = 0 + 2.8125 Reorder the terms: -2.8125 + 2.8125 + -3.75t + t2 = 0 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + -3.75t + t2 = 0 + 2.8125 -3.75t + t2 = 0 + 2.8125 Combine like terms: 0 + 2.8125 = 2.8125 -3.75t + t2 = 2.8125 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 = 2.8125 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = 2.8125 + 3.515625 Combine like terms: 2.8125 + 3.515625 = 6.328125 3.515625 + -3.75t + t2 = 6.328125 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 6.328125 Calculate the square root of the right side: 2.515576475 Break this problem into two subproblems by setting (t + -1.875) equal to 2.515576475 and -2.515576475.Subproblem 1
t + -1.875 = 2.515576475 Simplifying t + -1.875 = 2.515576475 Reorder the terms: -1.875 + t = 2.515576475 Solving -1.875 + t = 2.515576475 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 = 2.515576475 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 2.515576475 + 1.875 t = 2.515576475 + 1.875 Combine like terms: 2.515576475 + 1.875 = 4.390576475 t = 4.390576475 Simplifying t = 4.390576475Subproblem 2
t + -1.875 = -2.515576475 Simplifying t + -1.875 = -2.515576475 Reorder the terms: -1.875 + t = -2.515576475 Solving -1.875 + t = -2.515576475 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 = -2.515576475 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -2.515576475 + 1.875 t = -2.515576475 + 1.875 Combine like terms: -2.515576475 + 1.875 = -0.640576475 t = -0.640576475 Simplifying t = -0.640576475Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.390576475, -0.640576475}
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