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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 = 0.703125 3.515625 + -3.75t + t2 = 0.703125 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 0.703125 Calculate the square root of the right side: 0.838525492 Break this problem into two subproblems by setting (t + -1.875) equal to 0.838525492 and -0.838525492.Subproblem 1
t + -1.875 = 0.838525492 Simplifying t + -1.875 = 0.838525492 Reorder the terms: -1.875 + t = 0.838525492 Solving -1.875 + t = 0.838525492 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 = 0.838525492 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 0.838525492 + 1.875 t = 0.838525492 + 1.875 Combine like terms: 0.838525492 + 1.875 = 2.713525492 t = 2.713525492 Simplifying t = 2.713525492Subproblem 2
t + -1.875 = -0.838525492 Simplifying t + -1.875 = -0.838525492 Reorder the terms: -1.875 + t = -0.838525492 Solving -1.875 + t = -0.838525492 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 = -0.838525492 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -0.838525492 + 1.875 t = -0.838525492 + 1.875 Combine like terms: -0.838525492 + 1.875 = 1.036474508 t = 1.036474508 Simplifying t = 1.036474508Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.713525492, 1.036474508}
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