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Simplifying 16t2 + 64t + 3 = 0 Reorder the terms: 3 + 64t + 16t2 = 0 Solving 3 + 64t + 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'. 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 = -0.047437581 t = -0.047437581 Simplifying t = -0.047437581Subproblem 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 = -3.952562419 t = -3.952562419 Simplifying t = -3.952562419Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.047437581, -3.952562419}
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