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Simplifying -16.1t2 + 33t + 10 = 0 Reorder the terms: 10 + 33t + -16.1t2 = 0 Solving 10 + 33t + -16.1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16.1 the coefficient of the squared term: Divide each side by '-16.1'. -0.6211180124 + -2.049689441t + t2 = 0 Move the constant term to the right: Add '0.6211180124' to each side of the equation. -0.6211180124 + -2.049689441t + 0.6211180124 + t2 = 0 + 0.6211180124 Reorder the terms: -0.6211180124 + 0.6211180124 + -2.049689441t + t2 = 0 + 0.6211180124 Combine like terms: -0.6211180124 + 0.6211180124 = 0.0000000000 0.0000000000 + -2.049689441t + t2 = 0 + 0.6211180124 -2.049689441t + t2 = 0 + 0.6211180124 Combine like terms: 0 + 0.6211180124 = 0.6211180124 -2.049689441t + t2 = 0.6211180124 The t term is -2.049689441t. Take half its coefficient (-1.024844721). Square it (1.050306702) and add it to both sides. Add '1.050306702' to each side of the equation. -2.049689441t + 1.050306702 + t2 = 0.6211180124 + 1.050306702 Reorder the terms: 1.050306702 + -2.049689441t + t2 = 0.6211180124 + 1.050306702 Combine like terms: 0.6211180124 + 1.050306702 = 1.6714247144 1.050306702 + -2.049689441t + t2 = 1.6714247144 Factor a perfect square on the left side: (t + -1.024844721)(t + -1.024844721) = 1.6714247144 Calculate the square root of the right side: 1.292835919 Break this problem into two subproblems by setting (t + -1.024844721) equal to 1.292835919 and -1.292835919.Subproblem 1
t + -1.024844721 = 1.292835919 Simplifying t + -1.024844721 = 1.292835919 Reorder the terms: -1.024844721 + t = 1.292835919 Solving -1.024844721 + t = 1.292835919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.024844721' to each side of the equation. -1.024844721 + 1.024844721 + t = 1.292835919 + 1.024844721 Combine like terms: -1.024844721 + 1.024844721 = 0.000000000 0.000000000 + t = 1.292835919 + 1.024844721 t = 1.292835919 + 1.024844721 Combine like terms: 1.292835919 + 1.024844721 = 2.31768064 t = 2.31768064 Simplifying t = 2.31768064Subproblem 2
t + -1.024844721 = -1.292835919 Simplifying t + -1.024844721 = -1.292835919 Reorder the terms: -1.024844721 + t = -1.292835919 Solving -1.024844721 + t = -1.292835919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.024844721' to each side of the equation. -1.024844721 + 1.024844721 + t = -1.292835919 + 1.024844721 Combine like terms: -1.024844721 + 1.024844721 = 0.000000000 0.000000000 + t = -1.292835919 + 1.024844721 t = -1.292835919 + 1.024844721 Combine like terms: -1.292835919 + 1.024844721 = -0.267991198 t = -0.267991198 Simplifying t = -0.267991198Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.31768064, -0.267991198}
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