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Simplifying 4.905t2 + -7t + 0.65 = 0 Reorder the terms: 0.65 + -7t + 4.905t2 = 0 Solving 0.65 + -7t + 4.905t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. 0.1325178389 + -1.427115189t + t2 = 0 Move the constant term to the right: Add '-0.1325178389' to each side of the equation. 0.1325178389 + -1.427115189t + -0.1325178389 + t2 = 0 + -0.1325178389 Reorder the terms: 0.1325178389 + -0.1325178389 + -1.427115189t + t2 = 0 + -0.1325178389 Combine like terms: 0.1325178389 + -0.1325178389 = 0.0000000000 0.0000000000 + -1.427115189t + t2 = 0 + -0.1325178389 -1.427115189t + t2 = 0 + -0.1325178389 Combine like terms: 0 + -0.1325178389 = -0.1325178389 -1.427115189t + t2 = -0.1325178389 The t term is -1.427115189t. Take half its coefficient (-0.7135575945). Square it (0.5091644407) and add it to both sides. Add '0.5091644407' to each side of the equation. -1.427115189t + 0.5091644407 + t2 = -0.1325178389 + 0.5091644407 Reorder the terms: 0.5091644407 + -1.427115189t + t2 = -0.1325178389 + 0.5091644407 Combine like terms: -0.1325178389 + 0.5091644407 = 0.3766466018 0.5091644407 + -1.427115189t + t2 = 0.3766466018 Factor a perfect square on the left side: (t + -0.7135575945)(t + -0.7135575945) = 0.3766466018 Calculate the square root of the right side: 0.613715408 Break this problem into two subproblems by setting (t + -0.7135575945) equal to 0.613715408 and -0.613715408.Subproblem 1
t + -0.7135575945 = 0.613715408 Simplifying t + -0.7135575945 = 0.613715408 Reorder the terms: -0.7135575945 + t = 0.613715408 Solving -0.7135575945 + t = 0.613715408 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7135575945' to each side of the equation. -0.7135575945 + 0.7135575945 + t = 0.613715408 + 0.7135575945 Combine like terms: -0.7135575945 + 0.7135575945 = 0.0000000000 0.0000000000 + t = 0.613715408 + 0.7135575945 t = 0.613715408 + 0.7135575945 Combine like terms: 0.613715408 + 0.7135575945 = 1.3272730025 t = 1.3272730025 Simplifying t = 1.3272730025Subproblem 2
t + -0.7135575945 = -0.613715408 Simplifying t + -0.7135575945 = -0.613715408 Reorder the terms: -0.7135575945 + t = -0.613715408 Solving -0.7135575945 + t = -0.613715408 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7135575945' to each side of the equation. -0.7135575945 + 0.7135575945 + t = -0.613715408 + 0.7135575945 Combine like terms: -0.7135575945 + 0.7135575945 = 0.0000000000 0.0000000000 + t = -0.613715408 + 0.7135575945 t = -0.613715408 + 0.7135575945 Combine like terms: -0.613715408 + 0.7135575945 = 0.0998421865 t = 0.0998421865 Simplifying t = 0.0998421865Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.3272730025, 0.0998421865}
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