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Simplifying 4t2 + 1t + -4 = 0 Reorder the terms: -4 + 1t + 4t2 = 0 Solving -4 + 1t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + 0.25t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.25t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + 0.25t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.25t + t2 = 0 + 1 0.25t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.25t + t2 = 1 The t term is 0.25t. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25t + 0.015625 + t2 = 1 + 0.015625 Reorder the terms: 0.015625 + 0.25t + t2 = 1 + 0.015625 Combine like terms: 1 + 0.015625 = 1.015625 0.015625 + 0.25t + t2 = 1.015625 Factor a perfect square on the left side: (t + 0.125)(t + 0.125) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (t + 0.125) equal to 1.007782219 and -1.007782219.Subproblem 1
t + 0.125 = 1.007782219 Simplifying t + 0.125 = 1.007782219 Reorder the terms: 0.125 + t = 1.007782219 Solving 0.125 + t = 1.007782219 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = 1.007782219 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = 1.007782219 + -0.125 t = 1.007782219 + -0.125 Combine like terms: 1.007782219 + -0.125 = 0.882782219 t = 0.882782219 Simplifying t = 0.882782219Subproblem 2
t + 0.125 = -1.007782219 Simplifying t + 0.125 = -1.007782219 Reorder the terms: 0.125 + t = -1.007782219 Solving 0.125 + t = -1.007782219 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = -1.007782219 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = -1.007782219 + -0.125 t = -1.007782219 + -0.125 Combine like terms: -1.007782219 + -0.125 = -1.132782219 t = -1.132782219 Simplifying t = -1.132782219Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.882782219, -1.132782219}
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