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Simplifying 130 = -16t2 + 169t + 86 Reorder the terms: 130 = 86 + 169t + -16t2 Solving 130 = 86 + 169t + -16t2 Solving for variable 't'. Combine like terms: 130 + -86 = 44 44 + -169t + 16t2 = 86 + 169t + -16t2 + -86 + -169t + 16t2 Reorder the terms: 44 + -169t + 16t2 = 86 + -86 + 169t + -169t + -16t2 + 16t2 Combine like terms: 86 + -86 = 0 44 + -169t + 16t2 = 0 + 169t + -169t + -16t2 + 16t2 44 + -169t + 16t2 = 169t + -169t + -16t2 + 16t2 Combine like terms: 169t + -169t = 0 44 + -169t + 16t2 = 0 + -16t2 + 16t2 44 + -169t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 44 + -169t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.75 + -10.5625t + t2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -10.5625t + -2.75 + t2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -10.5625t + t2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -10.5625t + t2 = 0 + -2.75 -10.5625t + t2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -10.5625t + t2 = -2.75 The t term is -10.5625t. Take half its coefficient (-5.28125). Square it (27.89160156) and add it to both sides. Add '27.89160156' to each side of the equation. -10.5625t + 27.89160156 + t2 = -2.75 + 27.89160156 Reorder the terms: 27.89160156 + -10.5625t + t2 = -2.75 + 27.89160156 Combine like terms: -2.75 + 27.89160156 = 25.14160156 27.89160156 + -10.5625t + t2 = 25.14160156 Factor a perfect square on the left side: (t + -5.28125)(t + -5.28125) = 25.14160156 Calculate the square root of the right side: 5.014140162 Break this problem into two subproblems by setting (t + -5.28125) equal to 5.014140162 and -5.014140162.Subproblem 1
t + -5.28125 = 5.014140162 Simplifying t + -5.28125 = 5.014140162 Reorder the terms: -5.28125 + t = 5.014140162 Solving -5.28125 + t = 5.014140162 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.28125' to each side of the equation. -5.28125 + 5.28125 + t = 5.014140162 + 5.28125 Combine like terms: -5.28125 + 5.28125 = 0.00000 0.00000 + t = 5.014140162 + 5.28125 t = 5.014140162 + 5.28125 Combine like terms: 5.014140162 + 5.28125 = 10.295390162 t = 10.295390162 Simplifying t = 10.295390162Subproblem 2
t + -5.28125 = -5.014140162 Simplifying t + -5.28125 = -5.014140162 Reorder the terms: -5.28125 + t = -5.014140162 Solving -5.28125 + t = -5.014140162 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.28125' to each side of the equation. -5.28125 + 5.28125 + t = -5.014140162 + 5.28125 Combine like terms: -5.28125 + 5.28125 = 0.00000 0.00000 + t = -5.014140162 + 5.28125 t = -5.014140162 + 5.28125 Combine like terms: -5.014140162 + 5.28125 = 0.267109838 t = 0.267109838 Simplifying t = 0.267109838Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.295390162, 0.267109838}
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