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Simplifying -16t2 + -15t + 50 = 6 Reorder the terms: 50 + -15t + -16t2 = 6 Solving 50 + -15t + -16t2 = 6 Solving for variable 't'. Reorder the terms: 50 + -6 + -15t + -16t2 = 6 + -6 Combine like terms: 50 + -6 = 44 44 + -15t + -16t2 = 6 + -6 Combine like terms: 6 + -6 = 0 44 + -15t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.75 + 0.9375t + t2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 0.9375t + 2.75 + t2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 0.9375t + t2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 0.9375t + t2 = 0 + 2.75 0.9375t + t2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 0.9375t + t2 = 2.75 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 = 2.75 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375t + t2 = 2.75 + 0.2197265625 Combine like terms: 2.75 + 0.2197265625 = 2.9697265625 0.2197265625 + 0.9375t + t2 = 2.9697265625 Factor a perfect square on the left side: (t + 0.46875)(t + 0.46875) = 2.9697265625 Calculate the square root of the right side: 1.72328946 Break this problem into two subproblems by setting (t + 0.46875) equal to 1.72328946 and -1.72328946.Subproblem 1
t + 0.46875 = 1.72328946 Simplifying t + 0.46875 = 1.72328946 Reorder the terms: 0.46875 + t = 1.72328946 Solving 0.46875 + t = 1.72328946 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 = 1.72328946 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = 1.72328946 + -0.46875 t = 1.72328946 + -0.46875 Combine like terms: 1.72328946 + -0.46875 = 1.25453946 t = 1.25453946 Simplifying t = 1.25453946Subproblem 2
t + 0.46875 = -1.72328946 Simplifying t + 0.46875 = -1.72328946 Reorder the terms: 0.46875 + t = -1.72328946 Solving 0.46875 + t = -1.72328946 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 = -1.72328946 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = -1.72328946 + -0.46875 t = -1.72328946 + -0.46875 Combine like terms: -1.72328946 + -0.46875 = -2.19203946 t = -2.19203946 Simplifying t = -2.19203946Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.25453946, -2.19203946}
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