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Simplifying -16t2 + 64t = 3 Reorder the terms: 64t + -16t2 = 3 Solving 64t + -16t2 = 3 Solving for variable 't'. Reorder the terms: -3 + 64t + -16t2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 64t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.1875 + -4t + t2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -4t + -0.1875 + t2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -4t + t2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -4t + t2 = 0 + -0.1875 -4t + t2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -4t + t2 = -0.1875 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -0.1875 + 4 Reorder the terms: 4 + -4t + t2 = -0.1875 + 4 Combine like terms: -0.1875 + 4 = 3.8125 4 + -4t + t2 = 3.8125 Factor a perfect square on the left side: (t + -2)(t + -2) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (t + -2) equal to 1.952562419 and -1.952562419.Subproblem 1
t + -2 = 1.952562419 Simplifying t + -2 = 1.952562419 Reorder the terms: -2 + t = 1.952562419 Solving -2 + t = 1.952562419 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.952562419 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.952562419 + 2 t = 1.952562419 + 2 Combine like terms: 1.952562419 + 2 = 3.952562419 t = 3.952562419 Simplifying t = 3.952562419Subproblem 2
t + -2 = -1.952562419 Simplifying t + -2 = -1.952562419 Reorder the terms: -2 + t = -1.952562419 Solving -2 + t = -1.952562419 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.952562419 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.952562419 + 2 t = -1.952562419 + 2 Combine like terms: -1.952562419 + 2 = 0.047437581 t = 0.047437581 Simplifying t = 0.047437581Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.952562419, 0.047437581}
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