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Simplifying 0 = -16t2 + -15t + 100 Reorder the terms: 0 = 100 + -15t + -16t2 Solving 0 = 100 + -15t + -16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + 15t + 16t2 = 100 + -15t + -16t2 + -100 + 15t + 16t2 Reorder the terms: -100 + 15t + 16t2 = 100 + -100 + -15t + 15t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + 15t + 16t2 = 0 + -15t + 15t + -16t2 + 16t2 -100 + 15t + 16t2 = -15t + 15t + -16t2 + 16t2 Combine like terms: -15t + 15t = 0 -100 + 15t + 16t2 = 0 + -16t2 + 16t2 -100 + 15t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + 15t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.25 + 0.9375t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 0.9375t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 0.9375t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 0.9375t + t2 = 0 + 6.25 0.9375t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 0.9375t + t2 = 6.25 The t term is 0.9375t. Take half its coefficient (0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. 0.9375t + 0.2197265625 + t2 = 6.25 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375t + t2 = 6.25 + 0.2197265625 Combine like terms: 6.25 + 0.2197265625 = 6.4697265625 0.2197265625 + 0.9375t + t2 = 6.4697265625 Factor a perfect square on the left side: (t + 0.46875)(t + 0.46875) = 6.4697265625 Calculate the square root of the right side: 2.543565718 Break this problem into two subproblems by setting (t + 0.46875) equal to 2.543565718 and -2.543565718.Subproblem 1
t + 0.46875 = 2.543565718 Simplifying t + 0.46875 = 2.543565718 Reorder the terms: 0.46875 + t = 2.543565718 Solving 0.46875 + t = 2.543565718 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = 2.543565718 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = 2.543565718 + -0.46875 t = 2.543565718 + -0.46875 Combine like terms: 2.543565718 + -0.46875 = 2.074815718 t = 2.074815718 Simplifying t = 2.074815718Subproblem 2
t + 0.46875 = -2.543565718 Simplifying t + 0.46875 = -2.543565718 Reorder the terms: 0.46875 + t = -2.543565718 Solving 0.46875 + t = -2.543565718 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = -2.543565718 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = -2.543565718 + -0.46875 t = -2.543565718 + -0.46875 Combine like terms: -2.543565718 + -0.46875 = -3.012315718 t = -3.012315718 Simplifying t = -3.012315718Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.074815718, -3.012315718}
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