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Simplifying -16t2 + 26t = 5 Reorder the terms: 26t + -16t2 = 5 Solving 26t + -16t2 = 5 Solving for variable 't'. Reorder the terms: -5 + 26t + -16t2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 26t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.3125 + -1.625t + t2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -1.625t + -0.3125 + t2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -1.625t + t2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -1.625t + t2 = 0 + -0.3125 -1.625t + t2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -1.625t + t2 = -0.3125 The t term is -1.625t. Take half its coefficient (-0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. -1.625t + 0.66015625 + t2 = -0.3125 + 0.66015625 Reorder the terms: 0.66015625 + -1.625t + t2 = -0.3125 + 0.66015625 Combine like terms: -0.3125 + 0.66015625 = 0.34765625 0.66015625 + -1.625t + t2 = 0.34765625 Factor a perfect square on the left side: (t + -0.8125)(t + -0.8125) = 0.34765625 Calculate the square root of the right side: 0.589623821 Break this problem into two subproblems by setting (t + -0.8125) equal to 0.589623821 and -0.589623821.Subproblem 1
t + -0.8125 = 0.589623821 Simplifying t + -0.8125 = 0.589623821 Reorder the terms: -0.8125 + t = 0.589623821 Solving -0.8125 + t = 0.589623821 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + t = 0.589623821 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + t = 0.589623821 + 0.8125 t = 0.589623821 + 0.8125 Combine like terms: 0.589623821 + 0.8125 = 1.402123821 t = 1.402123821 Simplifying t = 1.402123821Subproblem 2
t + -0.8125 = -0.589623821 Simplifying t + -0.8125 = -0.589623821 Reorder the terms: -0.8125 + t = -0.589623821 Solving -0.8125 + t = -0.589623821 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + t = -0.589623821 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + t = -0.589623821 + 0.8125 t = -0.589623821 + 0.8125 Combine like terms: -0.589623821 + 0.8125 = 0.222876179 t = 0.222876179 Simplifying t = 0.222876179Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.402123821, 0.222876179}
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