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Simplifying -5.9 = -1.9t + -4.9t2 Solving -5.9 = -1.9t + -4.9t2 Solving for variable 't'. Reorder the terms: -5.9 + 1.9t + 4.9t2 = -1.9t + 1.9t + -4.9t2 + 4.9t2 Combine like terms: -1.9t + 1.9t = 0.0 -5.9 + 1.9t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -5.9 + 1.9t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -5.9 + 1.9t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.204081633 + 0.387755102t + t2 = 0 Move the constant term to the right: Add '1.204081633' to each side of the equation. -1.204081633 + 0.387755102t + 1.204081633 + t2 = 0 + 1.204081633 Reorder the terms: -1.204081633 + 1.204081633 + 0.387755102t + t2 = 0 + 1.204081633 Combine like terms: -1.204081633 + 1.204081633 = 0.000000000 0.000000000 + 0.387755102t + t2 = 0 + 1.204081633 0.387755102t + t2 = 0 + 1.204081633 Combine like terms: 0 + 1.204081633 = 1.204081633 0.387755102t + t2 = 1.204081633 The t term is 0.387755102t. Take half its coefficient (0.193877551). Square it (0.03758850478) and add it to both sides. Add '0.03758850478' to each side of the equation. 0.387755102t + 0.03758850478 + t2 = 1.204081633 + 0.03758850478 Reorder the terms: 0.03758850478 + 0.387755102t + t2 = 1.204081633 + 0.03758850478 Combine like terms: 1.204081633 + 0.03758850478 = 1.24167013778 0.03758850478 + 0.387755102t + t2 = 1.24167013778 Factor a perfect square on the left side: (t + 0.193877551)(t + 0.193877551) = 1.24167013778 Calculate the square root of the right side: 1.114302534 Break this problem into two subproblems by setting (t + 0.193877551) equal to 1.114302534 and -1.114302534.Subproblem 1
t + 0.193877551 = 1.114302534 Simplifying t + 0.193877551 = 1.114302534 Reorder the terms: 0.193877551 + t = 1.114302534 Solving 0.193877551 + t = 1.114302534 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.193877551' to each side of the equation. 0.193877551 + -0.193877551 + t = 1.114302534 + -0.193877551 Combine like terms: 0.193877551 + -0.193877551 = 0.000000000 0.000000000 + t = 1.114302534 + -0.193877551 t = 1.114302534 + -0.193877551 Combine like terms: 1.114302534 + -0.193877551 = 0.920424983 t = 0.920424983 Simplifying t = 0.920424983Subproblem 2
t + 0.193877551 = -1.114302534 Simplifying t + 0.193877551 = -1.114302534 Reorder the terms: 0.193877551 + t = -1.114302534 Solving 0.193877551 + t = -1.114302534 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.193877551' to each side of the equation. 0.193877551 + -0.193877551 + t = -1.114302534 + -0.193877551 Combine like terms: 0.193877551 + -0.193877551 = 0.000000000 0.000000000 + t = -1.114302534 + -0.193877551 t = -1.114302534 + -0.193877551 Combine like terms: -1.114302534 + -0.193877551 = -1.308180085 t = -1.308180085 Simplifying t = -1.308180085Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.920424983, -1.308180085}
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