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Simplifying 0 = -1(16t2 + -1t + -25) Reorder the terms: 0 = -1(-25 + -1t + 16t2) 0 = (-25 * -1 + -1t * -1 + 16t2 * -1) 0 = (25 + 1t + -16t2) Solving 0 = 25 + 1t + -16t2 Solving for variable 't'. Combine like terms: 0 + -25 = -25 -25 + -1t + 16t2 = 25 + 1t + -16t2 + -25 + -1t + 16t2 Reorder the terms: -25 + -1t + 16t2 = 25 + -25 + 1t + -1t + -16t2 + 16t2 Combine like terms: 25 + -25 = 0 -25 + -1t + 16t2 = 0 + 1t + -1t + -16t2 + 16t2 -25 + -1t + 16t2 = 1t + -1t + -16t2 + 16t2 Combine like terms: 1t + -1t = 0 -25 + -1t + 16t2 = 0 + -16t2 + 16t2 -25 + -1t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -25 + -1t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + -0.0625t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -0.0625t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -0.0625t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -0.0625t + t2 = 0 + 1.5625 -0.0625t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -0.0625t + t2 = 1.5625 The t term is -0.0625t. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625t + 0.0009765625 + t2 = 1.5625 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625t + t2 = 1.5625 + 0.0009765625 Combine like terms: 1.5625 + 0.0009765625 = 1.5634765625 0.0009765625 + -0.0625t + t2 = 1.5634765625 Factor a perfect square on the left side: (t + -0.03125)(t + -0.03125) = 1.5634765625 Calculate the square root of the right side: 1.250390564 Break this problem into two subproblems by setting (t + -0.03125) equal to 1.250390564 and -1.250390564.Subproblem 1
t + -0.03125 = 1.250390564 Simplifying t + -0.03125 = 1.250390564 Reorder the terms: -0.03125 + t = 1.250390564 Solving -0.03125 + t = 1.250390564 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + t = 1.250390564 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + t = 1.250390564 + 0.03125 t = 1.250390564 + 0.03125 Combine like terms: 1.250390564 + 0.03125 = 1.281640564 t = 1.281640564 Simplifying t = 1.281640564Subproblem 2
t + -0.03125 = -1.250390564 Simplifying t + -0.03125 = -1.250390564 Reorder the terms: -0.03125 + t = -1.250390564 Solving -0.03125 + t = -1.250390564 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + t = -1.250390564 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + t = -1.250390564 + 0.03125 t = -1.250390564 + 0.03125 Combine like terms: -1.250390564 + 0.03125 = -1.219140564 t = -1.219140564 Simplifying t = -1.219140564Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.281640564, -1.219140564}
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