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Simplifying 5(16t2 + -17.8t + -5) = 0 Reorder the terms: 5(-5 + -17.8t + 16t2) = 0 (-5 * 5 + -17.8t * 5 + 16t2 * 5) = 0 (-25 + -89t + 80t2) = 0 Solving -25 + -89t + 80t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 80 the coefficient of the squared term: Divide each side by '80'. -0.3125 + -1.1125t + t2 = 0.0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -1.1125t + 0.3125 + t2 = 0.0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -1.1125t + t2 = 0.0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -1.1125t + t2 = 0.0 + 0.3125 -1.1125t + t2 = 0.0 + 0.3125 Combine like terms: 0.0 + 0.3125 = 0.3125 -1.1125t + t2 = 0.3125 The t term is -1.1125t. Take half its coefficient (-0.55625). Square it (0.3094140625) and add it to both sides. Add '0.3094140625' to each side of the equation. -1.1125t + 0.3094140625 + t2 = 0.3125 + 0.3094140625 Reorder the terms: 0.3094140625 + -1.1125t + t2 = 0.3125 + 0.3094140625 Combine like terms: 0.3125 + 0.3094140625 = 0.6219140625 0.3094140625 + -1.1125t + t2 = 0.6219140625 Factor a perfect square on the left side: (t + -0.55625)(t + -0.55625) = 0.6219140625 Calculate the square root of the right side: 0.788615282 Break this problem into two subproblems by setting (t + -0.55625) equal to 0.788615282 and -0.788615282.Subproblem 1
t + -0.55625 = 0.788615282 Simplifying t + -0.55625 = 0.788615282 Reorder the terms: -0.55625 + t = 0.788615282 Solving -0.55625 + t = 0.788615282 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.55625' to each side of the equation. -0.55625 + 0.55625 + t = 0.788615282 + 0.55625 Combine like terms: -0.55625 + 0.55625 = 0.00000 0.00000 + t = 0.788615282 + 0.55625 t = 0.788615282 + 0.55625 Combine like terms: 0.788615282 + 0.55625 = 1.344865282 t = 1.344865282 Simplifying t = 1.344865282Subproblem 2
t + -0.55625 = -0.788615282 Simplifying t + -0.55625 = -0.788615282 Reorder the terms: -0.55625 + t = -0.788615282 Solving -0.55625 + t = -0.788615282 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.55625' to each side of the equation. -0.55625 + 0.55625 + t = -0.788615282 + 0.55625 Combine like terms: -0.55625 + 0.55625 = 0.00000 0.00000 + t = -0.788615282 + 0.55625 t = -0.788615282 + 0.55625 Combine like terms: -0.788615282 + 0.55625 = -0.232365282 t = -0.232365282 Simplifying t = -0.232365282Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.344865282, -0.232365282}
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