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Simplifying -16t2 + 15t + 50 = 0 Reorder the terms: 50 + 15t + -16t2 = 0 Solving 50 + 15t + -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'. -3.125 + -0.9375t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -0.9375t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -0.9375t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -0.9375t + t2 = 0 + 3.125 -0.9375t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -0.9375t + t2 = 3.125 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 = 3.125 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375t + t2 = 3.125 + 0.2197265625 Combine like terms: 3.125 + 0.2197265625 = 3.3447265625 0.2197265625 + -0.9375t + t2 = 3.3447265625 Factor a perfect square on the left side: (t + -0.46875)(t + -0.46875) = 3.3447265625 Calculate the square root of the right side: 1.828859361 Break this problem into two subproblems by setting (t + -0.46875) equal to 1.828859361 and -1.828859361.Subproblem 1
t + -0.46875 = 1.828859361 Simplifying t + -0.46875 = 1.828859361 Reorder the terms: -0.46875 + t = 1.828859361 Solving -0.46875 + t = 1.828859361 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 = 1.828859361 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = 1.828859361 + 0.46875 t = 1.828859361 + 0.46875 Combine like terms: 1.828859361 + 0.46875 = 2.297609361 t = 2.297609361 Simplifying t = 2.297609361Subproblem 2
t + -0.46875 = -1.828859361 Simplifying t + -0.46875 = -1.828859361 Reorder the terms: -0.46875 + t = -1.828859361 Solving -0.46875 + t = -1.828859361 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 = -1.828859361 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = -1.828859361 + 0.46875 t = -1.828859361 + 0.46875 Combine like terms: -1.828859361 + 0.46875 = -1.360109361 t = -1.360109361 Simplifying t = -1.360109361Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.297609361, -1.360109361}
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