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Simplifying -125 = 39.11t + (-4.9) * t2 Solving -125 = 39.11t + -4.9t2 Solving for variable 't'. Reorder the terms: -125 + -39.11t + 4.9t2 = 39.11t + -39.11t + -4.9t2 + 4.9t2 Combine like terms: 39.11t + -39.11t = 0.00 -125 + -39.11t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 -125 + -39.11t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -125 + -39.11t + 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'. -25.51020408 + -7.981632653t + t2 = 0 Move the constant term to the right: Add '25.51020408' to each side of the equation. -25.51020408 + -7.981632653t + 25.51020408 + t2 = 0 + 25.51020408 Reorder the terms: -25.51020408 + 25.51020408 + -7.981632653t + t2 = 0 + 25.51020408 Combine like terms: -25.51020408 + 25.51020408 = 0.00000000 0.00000000 + -7.981632653t + t2 = 0 + 25.51020408 -7.981632653t + t2 = 0 + 25.51020408 Combine like terms: 0 + 25.51020408 = 25.51020408 -7.981632653t + t2 = 25.51020408 The t term is -7.981632653t. Take half its coefficient (-3.990816327). Square it (15.92661496) and add it to both sides. Add '15.92661496' to each side of the equation. -7.981632653t + 15.92661496 + t2 = 25.51020408 + 15.92661496 Reorder the terms: 15.92661496 + -7.981632653t + t2 = 25.51020408 + 15.92661496 Combine like terms: 25.51020408 + 15.92661496 = 41.43681904 15.92661496 + -7.981632653t + t2 = 41.43681904 Factor a perfect square on the left side: (t + -3.990816327)(t + -3.990816327) = 41.43681904 Calculate the square root of the right side: 6.437143702 Break this problem into two subproblems by setting (t + -3.990816327) equal to 6.437143702 and -6.437143702.Subproblem 1
t + -3.990816327 = 6.437143702 Simplifying t + -3.990816327 = 6.437143702 Reorder the terms: -3.990816327 + t = 6.437143702 Solving -3.990816327 + t = 6.437143702 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.990816327' to each side of the equation. -3.990816327 + 3.990816327 + t = 6.437143702 + 3.990816327 Combine like terms: -3.990816327 + 3.990816327 = 0.000000000 0.000000000 + t = 6.437143702 + 3.990816327 t = 6.437143702 + 3.990816327 Combine like terms: 6.437143702 + 3.990816327 = 10.427960029 t = 10.427960029 Simplifying t = 10.427960029Subproblem 2
t + -3.990816327 = -6.437143702 Simplifying t + -3.990816327 = -6.437143702 Reorder the terms: -3.990816327 + t = -6.437143702 Solving -3.990816327 + t = -6.437143702 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.990816327' to each side of the equation. -3.990816327 + 3.990816327 + t = -6.437143702 + 3.990816327 Combine like terms: -3.990816327 + 3.990816327 = 0.000000000 0.000000000 + t = -6.437143702 + 3.990816327 t = -6.437143702 + 3.990816327 Combine like terms: -6.437143702 + 3.990816327 = -2.446327375 t = -2.446327375 Simplifying t = -2.446327375Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.427960029, -2.446327375}
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