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Simplifying 16t2 + -28t + 5 = 0 Reorder the terms: 5 + -28t + 16t2 = 0 Solving 5 + -28t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.3125 + -1.75t + t2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -1.75t + -0.3125 + t2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -1.75t + t2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -1.75t + t2 = 0 + -0.3125 -1.75t + t2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -1.75t + t2 = -0.3125 The t term is -1.75t. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75t + 0.765625 + t2 = -0.3125 + 0.765625 Reorder the terms: 0.765625 + -1.75t + t2 = -0.3125 + 0.765625 Combine like terms: -0.3125 + 0.765625 = 0.453125 0.765625 + -1.75t + t2 = 0.453125 Factor a perfect square on the left side: (t + -0.875)(t + -0.875) = 0.453125 Calculate the square root of the right side: 0.673145601 Break this problem into two subproblems by setting (t + -0.875) equal to 0.673145601 and -0.673145601.Subproblem 1
t + -0.875 = 0.673145601 Simplifying t + -0.875 = 0.673145601 Reorder the terms: -0.875 + t = 0.673145601 Solving -0.875 + t = 0.673145601 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = 0.673145601 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = 0.673145601 + 0.875 t = 0.673145601 + 0.875 Combine like terms: 0.673145601 + 0.875 = 1.548145601 t = 1.548145601 Simplifying t = 1.548145601Subproblem 2
t + -0.875 = -0.673145601 Simplifying t + -0.875 = -0.673145601 Reorder the terms: -0.875 + t = -0.673145601 Solving -0.875 + t = -0.673145601 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = -0.673145601 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = -0.673145601 + 0.875 t = -0.673145601 + 0.875 Combine like terms: -0.673145601 + 0.875 = 0.201854399 t = 0.201854399 Simplifying t = 0.201854399Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.548145601, 0.201854399}
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