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Simplifying 125 = -16t2 + 125t + 4 Reorder the terms: 125 = 4 + 125t + -16t2 Solving 125 = 4 + 125t + -16t2 Solving for variable 't'. Combine like terms: 125 + -4 = 121 121 + -125t + 16t2 = 4 + 125t + -16t2 + -4 + -125t + 16t2 Reorder the terms: 121 + -125t + 16t2 = 4 + -4 + 125t + -125t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 121 + -125t + 16t2 = 0 + 125t + -125t + -16t2 + 16t2 121 + -125t + 16t2 = 125t + -125t + -16t2 + 16t2 Combine like terms: 125t + -125t = 0 121 + -125t + 16t2 = 0 + -16t2 + 16t2 121 + -125t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 121 + -125t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 7.5625 + -7.8125t + t2 = 0 Move the constant term to the right: Add '-7.5625' to each side of the equation. 7.5625 + -7.8125t + -7.5625 + t2 = 0 + -7.5625 Reorder the terms: 7.5625 + -7.5625 + -7.8125t + t2 = 0 + -7.5625 Combine like terms: 7.5625 + -7.5625 = 0.0000 0.0000 + -7.8125t + t2 = 0 + -7.5625 -7.8125t + t2 = 0 + -7.5625 Combine like terms: 0 + -7.5625 = -7.5625 -7.8125t + t2 = -7.5625 The t term is -7.8125t. Take half its coefficient (-3.90625). Square it (15.25878906) and add it to both sides. Add '15.25878906' to each side of the equation. -7.8125t + 15.25878906 + t2 = -7.5625 + 15.25878906 Reorder the terms: 15.25878906 + -7.8125t + t2 = -7.5625 + 15.25878906 Combine like terms: -7.5625 + 15.25878906 = 7.69628906 15.25878906 + -7.8125t + t2 = 7.69628906 Factor a perfect square on the left side: (t + -3.90625)(t + -3.90625) = 7.69628906 Calculate the square root of the right side: 2.77421864 Break this problem into two subproblems by setting (t + -3.90625) equal to 2.77421864 and -2.77421864.Subproblem 1
t + -3.90625 = 2.77421864 Simplifying t + -3.90625 = 2.77421864 Reorder the terms: -3.90625 + t = 2.77421864 Solving -3.90625 + t = 2.77421864 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.90625' to each side of the equation. -3.90625 + 3.90625 + t = 2.77421864 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = 2.77421864 + 3.90625 t = 2.77421864 + 3.90625 Combine like terms: 2.77421864 + 3.90625 = 6.68046864 t = 6.68046864 Simplifying t = 6.68046864Subproblem 2
t + -3.90625 = -2.77421864 Simplifying t + -3.90625 = -2.77421864 Reorder the terms: -3.90625 + t = -2.77421864 Solving -3.90625 + t = -2.77421864 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.90625' to each side of the equation. -3.90625 + 3.90625 + t = -2.77421864 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = -2.77421864 + 3.90625 t = -2.77421864 + 3.90625 Combine like terms: -2.77421864 + 3.90625 = 1.13203136 t = 1.13203136 Simplifying t = 1.13203136Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.68046864, 1.13203136}
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