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Simplifying 123 = -16t2 + 123t Reorder the terms: 123 = 123t + -16t2 Solving 123 = 123t + -16t2 Solving for variable 't'. Reorder the terms: 123 + -123t + 16t2 = 123t + -123t + -16t2 + 16t2 Combine like terms: 123t + -123t = 0 123 + -123t + 16t2 = 0 + -16t2 + 16t2 123 + -123t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 123 + -123t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 7.6875 + -7.6875t + t2 = 0 Move the constant term to the right: Add '-7.6875' to each side of the equation. 7.6875 + -7.6875t + -7.6875 + t2 = 0 + -7.6875 Reorder the terms: 7.6875 + -7.6875 + -7.6875t + t2 = 0 + -7.6875 Combine like terms: 7.6875 + -7.6875 = 0.0000 0.0000 + -7.6875t + t2 = 0 + -7.6875 -7.6875t + t2 = 0 + -7.6875 Combine like terms: 0 + -7.6875 = -7.6875 -7.6875t + t2 = -7.6875 The t term is -7.6875t. Take half its coefficient (-3.84375). Square it (14.77441406) and add it to both sides. Add '14.77441406' to each side of the equation. -7.6875t + 14.77441406 + t2 = -7.6875 + 14.77441406 Reorder the terms: 14.77441406 + -7.6875t + t2 = -7.6875 + 14.77441406 Combine like terms: -7.6875 + 14.77441406 = 7.08691406 14.77441406 + -7.6875t + t2 = 7.08691406 Factor a perfect square on the left side: (t + -3.84375)(t + -3.84375) = 7.08691406 Calculate the square root of the right side: 2.662125854 Break this problem into two subproblems by setting (t + -3.84375) equal to 2.662125854 and -2.662125854.Subproblem 1
t + -3.84375 = 2.662125854 Simplifying t + -3.84375 = 2.662125854 Reorder the terms: -3.84375 + t = 2.662125854 Solving -3.84375 + t = 2.662125854 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.84375' to each side of the equation. -3.84375 + 3.84375 + t = 2.662125854 + 3.84375 Combine like terms: -3.84375 + 3.84375 = 0.00000 0.00000 + t = 2.662125854 + 3.84375 t = 2.662125854 + 3.84375 Combine like terms: 2.662125854 + 3.84375 = 6.505875854 t = 6.505875854 Simplifying t = 6.505875854Subproblem 2
t + -3.84375 = -2.662125854 Simplifying t + -3.84375 = -2.662125854 Reorder the terms: -3.84375 + t = -2.662125854 Solving -3.84375 + t = -2.662125854 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.84375' to each side of the equation. -3.84375 + 3.84375 + t = -2.662125854 + 3.84375 Combine like terms: -3.84375 + 3.84375 = 0.00000 0.00000 + t = -2.662125854 + 3.84375 t = -2.662125854 + 3.84375 Combine like terms: -2.662125854 + 3.84375 = 1.181624146 t = 1.181624146 Simplifying t = 1.181624146Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.505875854, 1.181624146}
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