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Simplifying 19.302t2 + -139.302t + 124.14 = 0 Reorder the terms: 124.14 + -139.302t + 19.302t2 = 0 Solving 124.14 + -139.302t + 19.302t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 19.302 the coefficient of the squared term: Divide each side by '19.302'. 6.43145788 + -7.216972334t + t2 = 0 Move the constant term to the right: Add '-6.43145788' to each side of the equation. 6.43145788 + -7.216972334t + -6.43145788 + t2 = 0 + -6.43145788 Reorder the terms: 6.43145788 + -6.43145788 + -7.216972334t + t2 = 0 + -6.43145788 Combine like terms: 6.43145788 + -6.43145788 = 0.00000000 0.00000000 + -7.216972334t + t2 = 0 + -6.43145788 -7.216972334t + t2 = 0 + -6.43145788 Combine like terms: 0 + -6.43145788 = -6.43145788 -7.216972334t + t2 = -6.43145788 The t term is -7.216972334t. Take half its coefficient (-3.608486167). Square it (13.02117242) and add it to both sides. Add '13.02117242' to each side of the equation. -7.216972334t + 13.02117242 + t2 = -6.43145788 + 13.02117242 Reorder the terms: 13.02117242 + -7.216972334t + t2 = -6.43145788 + 13.02117242 Combine like terms: -6.43145788 + 13.02117242 = 6.58971454 13.02117242 + -7.216972334t + t2 = 6.58971454 Factor a perfect square on the left side: (t + -3.608486167)(t + -3.608486167) = 6.58971454 Calculate the square root of the right side: 2.56704393 Break this problem into two subproblems by setting (t + -3.608486167) equal to 2.56704393 and -2.56704393.Subproblem 1
t + -3.608486167 = 2.56704393 Simplifying t + -3.608486167 = 2.56704393 Reorder the terms: -3.608486167 + t = 2.56704393 Solving -3.608486167 + t = 2.56704393 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.608486167' to each side of the equation. -3.608486167 + 3.608486167 + t = 2.56704393 + 3.608486167 Combine like terms: -3.608486167 + 3.608486167 = 0.000000000 0.000000000 + t = 2.56704393 + 3.608486167 t = 2.56704393 + 3.608486167 Combine like terms: 2.56704393 + 3.608486167 = 6.175530097 t = 6.175530097 Simplifying t = 6.175530097Subproblem 2
t + -3.608486167 = -2.56704393 Simplifying t + -3.608486167 = -2.56704393 Reorder the terms: -3.608486167 + t = -2.56704393 Solving -3.608486167 + t = -2.56704393 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.608486167' to each side of the equation. -3.608486167 + 3.608486167 + t = -2.56704393 + 3.608486167 Combine like terms: -3.608486167 + 3.608486167 = 0.000000000 0.000000000 + t = -2.56704393 + 3.608486167 t = -2.56704393 + 3.608486167 Combine like terms: -2.56704393 + 3.608486167 = 1.041442237 t = 1.041442237 Simplifying t = 1.041442237Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.175530097, 1.041442237}
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